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Global existence of weak solutions to a Keller-Segel model with L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} initial data

Global existence of weak solutions to a Keller-Segel model with L1\documentclass[12pt]{minimal}... In this work, we analyze the global existence for the Keller-Segel model with initial data only in L1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^1$$\end{document}. Classical techniques to prove global existence that are based on estimates in L∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{\infty } $$\end{document} cannot be applied due to the lack of regularity, and a new approach must be considered to overcome these difficulties. Finally, we provide an example of non-existence of solution in the case where the initial data is only a bounded Radon measure. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL UNIVERSITA DI FERRARA Springer Journals

Global existence of weak solutions to a Keller-Segel model with L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} initial data

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References (45)

Publisher
Springer Journals
Copyright
Copyright © The Author(s) under exclusive license to Università degli Studi di Ferrara 2022
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/s11565-022-00401-0
Publisher site
See Article on Publisher Site

Abstract

In this work, we analyze the global existence for the Keller-Segel model with initial data only in L1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^1$$\end{document}. Classical techniques to prove global existence that are based on estimates in L∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L^{\infty } $$\end{document} cannot be applied due to the lack of regularity, and a new approach must be considered to overcome these difficulties. Finally, we provide an example of non-existence of solution in the case where the initial data is only a bounded Radon measure.

Journal

ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals

Published: May 1, 2023

Keywords: Keller-Segel; Chemotaxis; “j” technique; L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^1$$\end{document} initial data; Uniform integrability; 35D30; 35B45; 35K55; 35K57

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