---
res:
  bibo_abstract:
  - "<jats:title>Abstract</jats:title>\r\n               <jats:p>We consider the spatially
    2D version of the model $$\\begin{equation*} \\qquad\\quad\\left\\{ \\begin{array}{@{}rcll}
    n_t + u\\cdot\\nabla n &amp;=&amp; \\Delta n - \\nabla \\cdot \\big(nS(x,n,c)
    \\cdot \\nabla c \\big), \\qquad &amp;\\qquad x\\in \\Omega, \\ t&amp;gt;0, \\\\
    c_t + u\\cdot \\nabla c &amp;=&amp; \\Delta c - n f(c), \\qquad &amp;\\qquad x\\in
    \\Omega, \\ t&amp;gt;0, \\\\ u_t &amp;=&amp; \\Delta u + \\nabla P + n\\nabla\\phi,
    \\qquad \\nabla\\cdot u=0, \\qquad &amp;\\qquad x\\in \\Omega, \\ t&amp;gt;0,
    \\end{array} \\right. \\qquad \\qquad (\\star) \\end{equation*}$$for nutrient
    taxis processes, possibly interacting with liquid environments. Here the particular
    focus is on the situation when the chemotactic sensitivity $S$ is not a scalar
    function but rather attains general values in ${\\mathbb{R}}^{2\\times 2}$, thus
    accounting for rotational flux components in accordance with experimental findings
    and recent modeling approaches. Reflecting significant new challenges that mainly
    stem from apparent loss of energy-like structures, especially for initial data
    with large size, the knowledge on ($\\star$) so far seems essentially restricted
    to results on global existence of certain generalized solutions with possibly
    quite poor boundedness and regularity properties; widely unaddressed seem aspects
    related to possible effects of such non-diagonal taxis mechanisms on the qualitative
    solution behavior, especially with regard to the fundamental question whether
    spatial structures may thereby be supported. The present work answers the latter
    in the negative in the following sense: under the assumptions that the initial
    data $(n_0,c_0,u_0)$ and the parameter functions $S$, $f$, and $\\phi$ are sufficiently
    smooth, and that $S$ is bounded and $f$ is positive on $(0,\\infty )$ with $f(0)=0$,
    it is shown that any nontrivial of these solutions eventually becomes smooth and
    satisfies $$\\begin{equation*} n(\\cdot,t)\\to - \\int_\\Omega n_0, \\quad c(\\cdot,t)\\to
    0 \\quad \\text{and} \\quad u(\\cdot,t)\\to 0 \\qquad \\text{as} \\ t\\to\\infty,
    \\end{equation*}$$uniformly with respect to $x\\in \\Omega$. By not requiring
    any smallness condition on the initial data, the latter seems new even in the
    corresponding fluid-free version obtained on letting $u\\equiv 0$ in ($\\star$).</jats:p>@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Michael
      foaf_name: Winkler, Michael
      foaf_surname: Winkler
      foaf_workInfoHomepage: http://www.librecat.org/personId=31496
  bibo_doi: 10.1093/imrn/rnz056
  bibo_issue: '11'
  bibo_volume: 2021
  dct_date: 2019^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/1073-7928
  - http://id.crossref.org/issn/1687-0247
  dct_language: eng
  dct_publisher: Oxford University Press (OUP)@
  dct_title: Can Rotational Fluxes Impede the Tendency Toward Spatial Homogeneity
    in Nutrient Taxis(-Stokes) Systems?@
...