ε-Regularity theorem and its application to the blow-up solutions of Keller-Segel systems in higher dimensions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:364

Article

Sugiyama, Yoshie

关键词: epsilon-Regularity theorem;    Blow-up;    Singular set;    Hausdorff dimension;    Scale invariant;   

DOI  :  10.1016/j.jmaa.2009.11.019

来源: Elsevier

【 摘 要 】

Let us consider (KS)(m) below for all N >= 2 and general exponents m and q. In particular, the 2-D semi-linear case such as N = 2, m = 1 and q = 2 is included. We establish an e-regularity theorem for weak solutions. As an application, we give an extension criterion in C([0, T]; LN(g-m)/2 (R-N)) which coincides with a scaling invariant class of weak solutions associated with (KS)(m). In addition, the Hausdorff dimension of its singular set is zero if u is an element of L-infinity(0, T; LN(g-m)/2 (R-N)) and u(N(g-m)/2) is an element of C-w ([0, T]; L-1 (R-N)). (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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