@article{63219,
abstract = {{We introduce the framework of Bayesian relative belief that directly evaluates whether or not the experimental data at hand support a given hypothesis regarding a quantum system by directly comparing the prior and posterior probabilities for the hypothesis. In model-dimension certification tasks, we show that the relative-belief procedure typically chooses Hilbert spaces that are never smaller in dimension than those selected from optimizing a broad class of information criteria, including Akaike's criterion. As a concrete and focused exposition of this powerful evidence-based technique, we apply the relative-belief procedure to an important application: . In particular, just by comparing prior and posterior probabilities based on data, we demonstrate its capability of tracking multiphoton emissions using (realistically lossy) single-photon detectors in order to assess the actual quality of photon sources without making assumptions, thereby reliably safeguarding source integrity for general quantum-information and communication tasks with Bayesian reasoning. Finally, we discuss how relative belief can be exploited to carry out parametric model certification and estimate the total dimension of the quantum state for the combined (measured) physical and interacting external systems described by the Tavis-Cummings model.
Published by the American Physical Society
2024
}},
author = {{Teo, Y. S. and Shringarpure, S. U. and Jeong, H. and Prasannan, Nidhin and Brecht, Benjamin and Silberhorn, Christine and Evans, M. and Mogilevtsev, D. and Sánchez-Soto, L. L.}},
issn = {{2469-9926}},
journal = {{Physical Review A}},
number = {{1}},
publisher = {{American Physical Society (APS)}},
title = {{{Relative-belief inference in quantum information theory}}},
doi = {{10.1103/physreva.110.012231}},
volume = {{110}},
year = {{2024}},
}
@article{63216,
abstract = {{The characterization of the complex spectral amplitude, that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterization techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic Q −function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate (QPG), which directly yield the chronocyclic Q −function. We evaluate the complex spectral amplitude from the measured chronocyclic Q −function data with maximum likelihood estimation (MLE), which is the established technique for quantum state tomography. The MLE yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any a priori information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial for classical pulse characterization problems.}},
author = {{Bhattacharjee, Abhinandan and Folge, Patrick Fabian and Serino, Laura Maria and Řeháček, Jaroslav and Hradil, Zdeněk and Silberhorn, Christine and Brecht, Benjamin}},
issn = {{1094-4087}},
journal = {{Optics Express}},
number = {{3}},
publisher = {{Optica Publishing Group}},
title = {{{Pulse characterization at the single-photon level through chronocyclic Q-function measurements}}},
doi = {{10.1364/oe.540125}},
volume = {{33}},
year = {{2024}},
}
@article{63220,
abstract = {{Identifying a reasonably small Hilbert space that completely describes an unknown quantum state is crucial for efficient quantum information processing. We introduce a general dimension-certification protocol for both discrete and continuous variables that is fully evidence based, relying solely on the experimental data collected and no other unjustified assumptions whatsoever. Using the Bayesian concept of relative belief, we take the effective dimension of the state as the smallest one such that the posterior probability is larger than the prior, as dictated by the data. The posterior probabilities associated with the relative-belief ratios measure the strength of the evidence provide by these ratios so that we can assess whether there is weak or strong evidence in favor or against a particular dimension. Using experimental data from spectral-temporal and polarimetry measurements, we demonstrate how to correctly assign Bayesian plausible error bars for the obtained effective dimensions. This makes relative belief a conservative and easy-to-use model-selection method for any experiment.
Published by the American Physical Society
2024
}},
author = {{Teo, Y. S. and Shringarpure, S. U. and Jeong, H. and Prasannan, Nidhin and Brecht, Benjamin and Silberhorn, Christine and Evans, M. and Mogilevtsev, D. and Sánchez-Soto, L. L.}},
issn = {{0031-9007}},
journal = {{Physical Review Letters}},
number = {{5}},
publisher = {{American Physical Society (APS)}},
title = {{{Evidence-Based Certification of Quantum Dimensions}}},
doi = {{10.1103/physrevlett.133.050204}},
volume = {{133}},
year = {{2024}},
}
@article{54288,
abstract = {{The ability to apply user-chosen large-scale unitary operations with high fidelity to a quantum state is key to realizing future photonic quantum technologies. Here, we realize the implementation of programmable unitary operations on up to 64 frequency-bin modes. To benchmark the performance of our system, we probe different quantum walk unitary operations, in particular, Grover walks on four-dimensional hypercubes with similarities exceeding 95% and quantum walks with 400 steps on circles and finite lines with similarities of 98%. Our results open a path toward implementing high-quality unitary operations, which can form the basis for applications in complex tasks, such as Gaussian boson sampling.
Published by the American Physical Society
2024
}},
author = {{De, Syamsundar and Ansari, Vahid and Sperling, Jan and Barkhofen, Sonja and Brecht, Benjamin and Silberhorn, Christine}},
issn = {{2643-1564}},
journal = {{Physical Review Research}},
number = {{2}},
publisher = {{American Physical Society (APS)}},
title = {{{Realization of high-fidelity unitary operations on up to 64 frequency bins}}},
doi = {{10.1103/physrevresearch.6.l022040}},
volume = {{6}},
year = {{2024}},
}
@article{63218,
abstract = {{Linear optical quantum networks, consisting of a quantum input state and a multiport interferometer, are an important building block for many quantum technological concepts, e.g., Gaussian boson sampling. Here, we propose the implementation of such networks based on frequency conversion by utilizing a so-called multioutput quantum pulse gate (MQPG). This approach allows the resource-efficient and therefore scalable implementation of frequency-bin-based, fully programmable interferometers in a single spatial and polarization mode. Quantum input states for this network can be provided by utilizing the strong frequency entanglement of a type-0 parametric down-conversion (PDC) source. Here, we develop a theoretical framework to describe linear networks based on an MQPG and PDC and utilize it to investigate the limits and scalabilty of our approach.
Published by the American Physical Society
2024
}},
author = {{Folge, Patrick Fabian and Stefszky, Michael and Brecht, Benjamin and Silberhorn, Christine}},
issn = {{2691-3399}},
journal = {{PRX Quantum}},
number = {{4}},
publisher = {{American Physical Society (APS)}},
title = {{{A Framework for Fully Programmable Frequency-Encoded Quantum Networks Harnessing Multioutput Quantum Pulse Gates}}},
doi = {{10.1103/prxquantum.5.040329}},
volume = {{5}},
year = {{2024}},
}
@article{63217,
abstract = {{We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and their superpositions. This device can facilitate practical realizations of quantum information applications such as high-dimensional quantum key distribution and thus enables secure communication with enhanced information capacity. We characterize the mode-sorter through a detector tomography in 3 and 5 dimensions and find a fidelity up to 0.958 ± 0.030 at the single-photon level.}},
author = {{Serino, Laura Maria and Eigner, Christof and Brecht, Benjamin and Silberhorn, Christine}},
issn = {{1094-4087}},
journal = {{Optics Express}},
number = {{3}},
publisher = {{Optica Publishing Group}},
title = {{{Programmable time-frequency mode-sorting of single photons with a multi-output quantum pulse gate}}},
doi = {{10.1364/oe.544206}},
volume = {{33}},
year = {{2024}},
}
@article{50840,
abstract = {{Superconducting nanowire single-photon detectors (SNSPDs) have been widely used to study the discrete nature of quantum states of light in the form of photon-counting experiments. We show that SNSPDs can also be used to study continuous variables of optical quantum states by performing homodyne detection at a bandwidth of 400 kHz. By measuring the interference of a continuous-wave field of a local oscillator with the field of the vacuum state using two SNSPDs, we show that the variance of the difference in count rates is linearly proportional to the photon flux of the local oscillator over almost five orders of magnitude. The resulting shot-noise clearance of (46.0 ± 1.1) dB is the highest reported clearance for a balanced optical homodyne detector, demonstrating their potential for measuring highly squeezed states in the continuous-wave regime. In addition, we measured a CMRR = 22.4 dB. From the joint click counting statistics, we also measure the phase-dependent quadrature of a weak coherent state to demonstrate our device’s functionality as a homodyne detector.}},
author = {{Protte, Maximilian and Schapeler, Timon and Sperling, Jan and Bartley, Tim}},
issn = {{2837-6714}},
journal = {{Optica Quantum}},
number = {{1}},
publisher = {{Optica Publishing Group}},
title = {{{Low-noise balanced homodyne detection with superconducting nanowire single-photon detectors}}},
doi = {{10.1364/opticaq.502201}},
volume = {{2}},
year = {{2024}},
}
@article{63227,
abstract = {{Using a precise electrochemical quartz crystal microbalance (EQCM), it was shown that electrogravimetry can be carried out with microelectrode arrays (MEAs). Significant differences between the potential dependent adsorption of a redox-active molecule and electroplating were presented.}},
author = {{Biermann, Michael and Leppin, Christian and Langhoff, Arne and Ziemer, Thorben and Rembe, Christian and Johannsmann, Diethelm}},
issn = {{0003-2654}},
journal = {{The Analyst}},
number = {{7}},
pages = {{2138--2146}},
publisher = {{Royal Society of Chemistry (RSC)}},
title = {{{An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition}}},
doi = {{10.1039/d3an02210b}},
volume = {{149}},
year = {{2024}},
}
@article{63264,
abstract = {{Abstract
In a smoothly bounded convex domain
Ω
⊂
R
n
${\Omega}\subset {\mathbb{R}}^{n}$
with n ≥ 1, a no-flux initial-boundary value problem for
u
t
=
Δ
u
ϕ
(
v
)
,
v
t
=
Δ
v
−
u
v
,
$$\begin{cases}_{t}={\Delta}\left(u\phi \left(v\right)\right),\quad \hfill \\ {v}_{t}={\Delta}v-uv,\quad \hfill \end{cases}$$
is considered under the assumption that near the origin, the function ϕ suitably generalizes the prototype given by
ϕ
(
ξ
)
=
ξ
α
,
ξ
∈
[
0
,
ξ
0
]
.
$$\phi \left(\xi \right)={\xi }^{\alpha },\qquad \xi \in \left[0,{\xi }_{0}\right].$$
By means of separate approaches, it is shown that in both cases α ∈ (0, 1) and α ∈ [1, 2] some global weak solutions exist which, inter alia, satisfy
C
(
T
)
≔
ess sup
t
∈
(
0
,
T
)
∫
Ω
u
(
⋅
,
t
)
ln
u
(
⋅
,
t
)
<
∞
for all
T
>
0
,
$$C\left(T\right){:=}\underset{t\in \left(0,T\right)}{\text{ess\,sup}}{\int }_{{\Omega}}u\left(\cdot ,t\right)\mathrm{ln}u\left(\cdot ,t\right){< }\infty \qquad \text{for\,all\,}T{ >}0,$$
with sup
T>0
C(T) < ∞ if α ∈ [1, 2].}},
author = {{Winkler, Michael}},
issn = {{2169-0375}},
journal = {{Advanced Nonlinear Studies}},
number = {{3}},
pages = {{592--615}},
publisher = {{Walter de Gruyter GmbH}},
title = {{{A degenerate migration-consumption model in domains of arbitrary dimension}}},
doi = {{10.1515/ans-2023-0131}},
volume = {{24}},
year = {{2024}},
}
@article{63248,
abstract = {{Abstract
The Navier–Stokes system
$$\begin{aligned} \left\{ \begin{array}{l} u_t + (u\cdot \nabla ) u =\Delta u+\nabla P + f(x,t), \\ \nabla \cdot u=0, \end{array} \right. \end{aligned}$$
u
t
+
(
u
·
∇
)
u
=
Δ
u
+
∇
P
+
f
(
x
,
t
)
,
∇
·
u
=
0
,
is considered along with homogeneous Dirichlet boundary conditions in a smoothly bounded planar domain
$$\Omega $$
Ω
. It is firstly, inter alia, observed that if
$$T>0$$
T
>
0
and
$$\begin{aligned} \int _0^T \bigg \{ \int _\Omega |f(x,t)| \cdot \ln ^\frac{1}{2} \big (|f(x,t)|+1\big ) dx \bigg \}^2 dt <\infty , \end{aligned}$$
∫
0
T
{
∫
Ω
|
f
(
x
,
t
)
|
·
ln
1
2
(
|
f
(
x
,
t
)
|
+
1
)
d
x
}
2
d
t
<
∞
,
then for all divergence-free
$$u_0\in L^2(\Omega ;{\mathbb {R}}^2)$$
u
0
∈
L
2
(
Ω
;
R
2
)
, a corresponding initial-boundary value problem admits a weak solution u with
$$u|_{t=0}=u_0$$
u
|
t
=
0
=
u
0
. For any positive and nondecreasing
$$L\in C^0([0,\infty ))$$
L
∈
C
0
(
[
0
,
∞
)
)
such that
$$\begin{aligned} \frac{L(\xi )}{\ln ^\frac{1}{2} \xi } \rightarrow 0 \qquad \text{ as } \xi \rightarrow \infty , \end{aligned}$$
L
(
ξ
)
ln
1
2
ξ
→
0
as
ξ
→
∞
,
this is complemented by a statement on nonexistence of such a solution in the presence of smooth initial data and a suitably constructed
$$f:\Omega \times (0,T)\rightarrow {\mathbb {R}}^2$$
f
:
Ω
×
(
0
,
T
)
→
R
2
fulfilling
$$\begin{aligned} \int _0^T \bigg \{ \int _\Omega |f(x,t)| \cdot L\big (|f(x,t)|\big ) dx \bigg \}^2 dt < \infty . \end{aligned}$$
∫
0
T
{
∫
Ω
|
f
(
x
,
t
)
|
·
L
(
|
f
(
x
,
t
)
|
)
d
x
}
2
d
t
<
∞
.
This resolves a fine structure in the borderline case
$$p=1$$
p
=
1
and
$$q=2$$
q
=
2
appearing in results on existence of weak solutions for sources in
$$L^q((0,T);L^p(\Omega ;{\mathbb {R}}^2))$$
L
q
(
(
0
,
T
)
;
L
p
(
Ω
;
R
2
)
)
when
$$p\in (1,\infty ]$$
p
∈
(
1
,
∞
]
and
$$q\in [1,\infty ]$$
q
∈
[
1
,
∞
]
satisfy
$$\frac{1}{p}+\frac{1}{q}\le \frac{3}{2}$$
1
p
+
1
q
≤
3
2
, and on nonexistence if here
$$p\in [1,\infty )$$
p
∈
[
1
,
∞
)
and
$$q\in [1,\infty )$$
q
∈
[
1
,
∞
)
are such that
$$\frac{1}{p}+\frac{1}{q}>\frac{3}{2}$$
1
p
+
1
q
>
3
2
.}},
author = {{Winkler, Michael}},
issn = {{0025-5831}},
journal = {{Mathematische Annalen}},
number = {{2}},
pages = {{3023--3054}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Externally forced blow-up and optimal spaces for source regularity in the two-dimensional Navier–Stokes system}}},
doi = {{10.1007/s00208-024-02987-6}},
volume = {{391}},
year = {{2024}},
}
@article{63245,
abstract = {{
A family of interpolation inequalities is derived, which differ from estimates of classical Gagliardo–Nirenberg type through the appearance of certain logarithmic deviations from standard Lebesgue norms in zero-order expressions. Optimality of the obtained inequalities is shown. A subsequent application reveals that when posed under homogeneous Neumann boundary conditions in smoothly bounded planar domains and with suitably regular initial data, for any choice of
\alpha>0
the Keller–Segel-type migration–consumption system
u_{t} = \Delta (uv^{-\alpha})
,
v_{t} = \Delta v-uv
, admits a global classical solution.
}},
author = {{Winkler, Michael}},
issn = {{0294-1449}},
journal = {{Annales de l'Institut Henri Poincaré C, Analyse non linéaire}},
number = {{6}},
pages = {{1601--1630}},
publisher = {{European Mathematical Society - EMS - Publishing House GmbH}},
title = {{{Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system}}},
doi = {{10.4171/aihpc/141}},
volume = {{42}},
year = {{2024}},
}
@article{63257,
abstract = {{AbstractThe quasilinear Keller–Segel system$$\begin{aligned} \left\{ \begin{array}{l} u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \\ v_t=\Delta v-v+u, \end{array}\right. \end{aligned}$$ut=∇·(D(u)∇u)-∇·(S(u)∇v),vt=Δv-v+u,endowed with homogeneous Neumann boundary conditions is considered in a bounded domain$$\Omega \subset {\mathbb {R}}^n$$Ω⊂Rn,$$n \ge 3$$n≥3, with smooth boundary for sufficiently regular functionsDandSsatisfying$$D>0$$D>0on$$[0,\infty )$$[0,∞),$$S>0$$S>0on$$(0,\infty )$$(0,∞)and$$S(0)=0$$S(0)=0. On the one hand, it is shown that if$$\frac{S}{D}$$SDsatisfies the subcritical growth condition$$\begin{aligned} \frac{S(s)}{D(s)} \le C s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha < \frac{2}{n} \end{aligned}$$S(s)D(s)≤Csαforalls≥1withsomeα<2nand$$C>0$$C>0, then for any sufficiently regular initial data there exists a global weak energy solution such that$${ \mathrm{{ess}}} \sup _{t>0} \Vert u(t) \Vert _{L^p(\Omega )}<\infty $$esssupt>0‖u(t)‖Lp(Ω)<∞for some$$p > \frac{2n}{n+2}$$p>2nn+2. On the other hand, if$$\frac{S}{D}$$SDsatisfies the supercritical growth condition$$\begin{aligned} \frac{S(s)}{D(s)} \ge c s^\alpha \qquad \text{ for } \text{ all } s\ge 1 \qquad \text{ with } \text{ some } \alpha > \frac{2}{n} \end{aligned}$$S(s)D(s)≥csαforalls≥1withsomeα>2nand$$c>0$$c>0, then the nonexistence of a global weak energy solution having the boundedness property stated above is shown for some initial data in the radial setting. This establishes some criticality of the value$$\alpha = \frac{2}{n}$$α=2nfor$$n \ge 3$$n≥3, without any additional assumption on the behavior ofD(s) as$$s \rightarrow \infty $$s→∞, in particular without requiring any algebraic lower bound forD. When applied to the Keller–Segel system with volume-filling effect for probability distribution functions of the type$$Q(s) = \exp (-s^\beta )$$Q(s)=exp(-sβ),$$s \ge 0$$s≥0, for global solvability the exponent$$\beta = \frac{n-2}{n}$$β=n-2nis seen to be critical.}},
author = {{Stinner, Christian and Winkler, Michael}},
issn = {{1424-3199}},
journal = {{Journal of Evolution Equations}},
number = {{2}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{A critical exponent in a quasilinear Keller–Segel system with arbitrarily fast decaying diffusivities accounting for volume-filling effects}}},
doi = {{10.1007/s00028-024-00954-x}},
volume = {{24}},
year = {{2024}},
}
@article{63253,
abstract = {{Abstract
The Neumann problem for the Keller-Segel system
{
u
t
=
∇
⋅
(
D
(
u
)
∇
u
)
−
∇
⋅
(
S
(
u
)
∇
v
)
,
0
=
Δ
v
−
μ
+
u
,
μ
=
−
∫
Ω
u
d
x
,
is considered in n-dimensional balls Ω with
n
⩾
2
, with suitably regular and radially symmetric, radially nonincreasing initial data u
0. The functions D and S are only assumed to belong to
C
2
(
[
0
,
∞
)
)
and to satisfy D > 0 and
S
⩾
0
on
[
0
,
∞
)
as well as
S
(
0
)
=
0
; in particular, diffusivities with arbitrarily fast decay are included.
In this general context, it is shown that it is merely the asymptotic behavior as
ξ
→
∞
of the expression
I
(
ξ
)
:=
S
(
ξ
)
ξ
2
n
D
(
ξ
)
,
ξ
>
0
,
which decides about the occurrence of blow-up: Namely, it is seen that
•
if
lim
ξ
→
∞
I
(
ξ
)
=
0
, then any such solution is global and bounded, that
•
if
lim sup
ξ
→
∞
I
(
ξ
)
<
∞
and
∫
Ω
u
0
is suitably small, then the corresponding solution is global and bounded, and that
•
if
lim inf
ξ
→
∞
I
(
ξ
)
>
0
, then at each appropriately large mass level m, there exist radial initial data u
0 such that
∫
Ω
u
0
=
m
, and that the associated solution blows up either in finite or in infinite time.
This especially reveals the presence of critical mass phenomena whenever
lim
ξ
→
∞
I
(
ξ
)
∈
(
0
,
∞
)
exists.}},
author = {{Ding, Mengyao and Winkler, Michael}},
issn = {{0951-7715}},
journal = {{Nonlinearity}},
number = {{12}},
publisher = {{IOP Publishing}},
title = {{{Radial blow-up in quasilinear Keller-Segel systems: approaching the full picture}}},
doi = {{10.1088/1361-6544/ad871a}},
volume = {{37}},
year = {{2024}},
}
@article{63254,
abstract = {{AbstractThe chemotaxis-Navier–Stokes system $$\begin{aligned} \left\{ \begin{array}{rcl} n_t+u\cdot \nabla n & =& \Delta \big (n c^{-\alpha } \big ), \\ c_t+ u\cdot \nabla c & =& \Delta c -nc,\\ u_t + (u\cdot \nabla ) u & =& \Delta u+\nabla P + n\nabla \Phi , \qquad \nabla \cdot u=0, \end{array} \right. \end{aligned}$$
n
t
+
u
·
∇
n
=
Δ
(
n
c
-
α
)
,
c
t
+
u
·
∇
c
=
Δ
c
-
n
c
,
u
t
+
(
u
·
∇
)
u
=
Δ
u
+
∇
P
+
n
∇
Φ
,
∇
·
u
=
0
,
modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain $$\Omega \subset \mathbb R^2$$
Ω
⊂
R
2
. For all $$\alpha > 0$$
α
>
0
and all sufficiently regular $$\Phi $$
Φ
, we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time $$L^p$$
L
p
estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time $$L^2$$
L
2
norm of the force term raised to an arbitrary small power.}},
author = {{Fuest, Mario and Winkler, Michael}},
issn = {{1422-6928}},
journal = {{Journal of Mathematical Fluid Mechanics}},
number = {{4}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Uniform $$L^p$$ Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing}}},
doi = {{10.1007/s00021-024-00899-8}},
volume = {{26}},
year = {{2024}},
}
@article{63259,
abstract = {{AbstractIn a smoothly bounded two‐dimensional domain and for a given nondecreasing positive unbounded , for each and the inequality
is shown to hold for any positive fulfilling
This is thereafter applied to nonglobal solutions of the Keller–Segel system coupled to the incompressible Navier–Stokes equations through transport and buoyancy, and it is seen that in any such blow‐up event the corresponding population density cannot remain uniformly integrable over near its explosion time.}},
author = {{Wang, Yulan and Winkler, Michael}},
issn = {{0024-6107}},
journal = {{Journal of the London Mathematical Society}},
number = {{3}},
publisher = {{Wiley}},
title = {{{An interpolation inequality involving LlogL$L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system}}},
doi = {{10.1112/jlms.12885}},
volume = {{109}},
year = {{2024}},
}
@article{63258,
abstract = {{This manuscript studies a no-flux initial-boundary value problem for a four-component chemotaxis system that has been proposed as a model for the response of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel type situations focusing on two-component interplay of chemotaxing populations with a signal directly secreted by themselves, the presently considered system accounts for a certain indirect mechanism of attractant evolution. Despite the presence of a zero-order exciting nonlinearity of quadratic type that forms a core mathematical feature of the model, the manuscript asserts the global existence of classical solutions for initial data of arbitrary size in three-dimensional domains.
}},
author = {{Tao, Youshan and Winkler, Michael}},
issn = {{0002-9939}},
journal = {{Proceedings of the American Mathematical Society}},
number = {{10}},
pages = {{4325--4341}},
publisher = {{American Mathematical Society (AMS)}},
title = {{{Global smooth solutions in a chemotaxis system modeling immune response to a solid tumor}}},
doi = {{10.1090/proc/16867}},
volume = {{152}},
year = {{2024}},
}
@article{63256,
author = {{Nikolić, Vanja and Winkler, Michael}},
issn = {{0362-546X}},
journal = {{Nonlinear Analysis}},
publisher = {{Elsevier BV}},
title = {{{L∞ blow-up in the Jordan–Moore–Gibson–Thompson equation}}},
doi = {{10.1016/j.na.2024.113600}},
volume = {{247}},
year = {{2024}},
}
@article{63260,
abstract = {{AbstractA no‐flux initial‐boundary value problem for
is considered in a ball , where and .Under the assumption that , it is shown that for each , there exist and a positive with the property that whenever is nonnegative with , the global solutions to () emanating from the initial data have the property that
}},
author = {{Wang, Yulan and Winkler, Michael}},
issn = {{0025-584X}},
journal = {{Mathematische Nachrichten}},
number = {{6}},
pages = {{2353--2364}},
publisher = {{Wiley}},
title = {{{A singular growth phenomenon in a Keller–Segel–type parabolic system involving density‐suppressed motilities}}},
doi = {{10.1002/mana.202300361}},
volume = {{297}},
year = {{2024}},
}
@article{63262,
abstract = {{AbstractRadially symmetric global unbounded solutions of the chemotaxis system $$\left\{ {\matrix{{{u_t} = \nabla \cdot (D(u)\nabla u) - \nabla \cdot (uS(u)\nabla v),} \hfill & {} \hfill \cr {0 = \Delta v - \mu + u,} \hfill & {\mu = {1 \over {|\Omega |}}\int_\Omega {u,} } \hfill \cr } } \right.$$
{
u
t
=
∇
⋅
(
D
(
u
)
∇
u
)
−
∇
⋅
(
u
S
(
u
)
∇
v
)
,
0
=
Δ
v
−
μ
+
u
,
μ
=
1
|
Ω
|
∫
Ω
u
,
are considered in a ball Ω = BR(0) ⊂ ℝn, where n ≥ 3 and R > 0.Under the assumption that D and S suitably generalize the prototypes given by D(ξ) = (ξ + ι)m−1 and S(ξ) = (ξ + 1)−λ−1 for all ξ > 0 and some m ∈ ℝ, λ >0 and ι ≥ 0 fulfilling $$m + \lambda < 1 - {2 \over n}$$
m
+
λ
<
1
−
2
n
, a considerably large set of initial data u0 is found to enforce a complete mass aggregation in infinite time in the sense that for any such u0, an associated Neumann type initial-boundary value problem admits a global classical solution (u, v) satisfying $${1 \over C} \cdot {(t + 1)^{{1 \over \lambda }}} \le ||u( \cdot ,t)|{|_{{L^\infty }(\Omega )}} \le C \cdot {(t + 1)^{{1 \over \lambda }}}\,\,\,{\rm{for}}\,\,{\rm{all}}\,\,t > 0$$
1
C
⋅
(
t
+
1
)
1
λ
≤
|
|
u
(
⋅
,
t
)
|
|
L
∞
(
Ω
)
≤
C
⋅
(
t
+
1
)
1
λ
f
o
r
a
l
l
t
>
0
as well as $$||u( \cdot \,,t)|{|_{{L^1}(\Omega \backslash {B_{{r_0}}}(0))}} \to 0\,\,\,{\rm{as}}\,\,t \to \infty \,\,\,{\rm{for}}\,\,{\rm{all}}\,\,{r_0} \in (0,R)$$
|
|
u
(
⋅
,
t
)
|
|
L
1
(
Ω
\
B
r
0
(
0
)
)
→
0
as
t
→
∞
for all
r
0
∈
(
0
,
R
)
with some C > 0.}},
author = {{Winkler, Michael}},
issn = {{0021-2172}},
journal = {{Israel Journal of Mathematics}},
number = {{1}},
pages = {{93--127}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Complete infinite-time mass aggregation in a quasilinear Keller–Segel system}}},
doi = {{10.1007/s11856-024-2618-9}},
volume = {{263}},
year = {{2024}},
}
@article{63263,
author = {{Winkler, Michael}},
issn = {{0022-0396}},
journal = {{Journal of Differential Equations}},
pages = {{423--456}},
publisher = {{Elsevier BV}},
title = {{{L∞ bounds in a two-dimensional doubly degenerate nutrient taxis system with general cross-diffusive flux}}},
doi = {{10.1016/j.jde.2024.04.028}},
volume = {{400}},
year = {{2024}},
}