{"date_updated":"2025-12-18T20:12:43Z","date_created":"2025-12-18T19:00:24Z","intvolume":"        42","type":"journal_article","publication_identifier":{"issn":["0294-1449","1873-1430"]},"volume":42,"author":[{"last_name":"Winkler","full_name":"Winkler, Michael","first_name":"Michael","id":"31496"}],"status":"public","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:p>\r\n            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 \r\n            <jats:inline-formula>\r\n              <jats:tex-math>\\alpha&gt;0</jats:tex-math>\r\n            </jats:inline-formula>\r\n             the Keller–Segel-type migration–consumption system \r\n            <jats:inline-formula>\r\n              <jats:tex-math>u_{t} = \\Delta (uv^{-\\alpha})</jats:tex-math>\r\n            </jats:inline-formula>\r\n            , \r\n            <jats:inline-formula>\r\n              <jats:tex-math>v_{t} = \\Delta v-uv</jats:tex-math>\r\n            </jats:inline-formula>\r\n            , admits a global classical solution.\r\n          </jats:p>","lang":"eng"}],"publication_status":"published","doi":"10.4171/aihpc/141","issue":"6","user_id":"31496","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","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","citation":{"ieee":"M. Winkler, “Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system,” <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>, vol. 42, no. 6, pp. 1601–1630, 2024, doi: <a href=\"https://doi.org/10.4171/aihpc/141\">10.4171/aihpc/141</a>.","mla":"Winkler, Michael. “Logarithmically Refined Gagliardo–Nirenberg Interpolation and Application to Blow-up Exclusion in a Singular Chemotaxis–Consumption System.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, vol. 42, no. 6, European Mathematical Society - EMS - Publishing House GmbH, 2024, pp. 1601–30, doi:<a href=\"https://doi.org/10.4171/aihpc/141\">10.4171/aihpc/141</a>.","bibtex":"@article{Winkler_2024, title={Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system}, volume={42}, DOI={<a href=\"https://doi.org/10.4171/aihpc/141\">10.4171/aihpc/141</a>}, number={6}, journal={Annales de l’Institut Henri Poincaré C, Analyse non linéaire}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Winkler, Michael}, year={2024}, pages={1601–1630} }","ama":"Winkler M. Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system. <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>. 2024;42(6):1601-1630. doi:<a href=\"https://doi.org/10.4171/aihpc/141\">10.4171/aihpc/141</a>","short":"M. Winkler, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 42 (2024) 1601–1630.","chicago":"Winkler, Michael. “Logarithmically Refined Gagliardo–Nirenberg Interpolation and Application to Blow-up Exclusion in a Singular Chemotaxis–Consumption System.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i> 42, no. 6 (2024): 1601–30. <a href=\"https://doi.org/10.4171/aihpc/141\">https://doi.org/10.4171/aihpc/141</a>.","apa":"Winkler, M. (2024). Logarithmically refined Gagliardo–Nirenberg interpolation and application to blow-up exclusion in a singular chemotaxis–consumption system. <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, <i>42</i>(6), 1601–1630. <a href=\"https://doi.org/10.4171/aihpc/141\">https://doi.org/10.4171/aihpc/141</a>"},"_id":"63245","page":"1601-1630","year":"2024"}