A Note on the Subcritical Two Dimensional Keller-Segel System |
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| Authors: | Jose A Carrillo Li Chen Jian-Guo Liu Jinhuan Wang |
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| Institution: | 1.ICREA and Departament de Matemàtiques,Universitat Autònoma de Barcelona,Bellaterra (Barcelona),Spain;2.Department of Mathematical Sciences,Tsinghua University,Beijing,P.R. China;3.Department of Physics and Department of Mathematics,Duke University,Durham,USA;4.Department of Mathematics,Liaoning University,Shenyang,P.R. China |
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| Abstract: | The existence of solution for the 2D-Keller-Segel system in the subcritical case, i.e. when the initial mass is less than
8π, is reproved. Instead of using the entropy in the free energy and free energy dissipation, which was used in the proofs (Blanchet
et al. in SIAM J. Numer. Anal. 46:691–721, 2008; Electron. J. Differ. Equ. Conf. 44:32, 2006 (electronic)), the potential energy term is fully utilized by adapting Delort’s theory on 2D incompressible Euler equation
(Delort in J. Am. Math. Soc. 4:553–386, 1991). |
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