End-point maximal regularity and its application to two-dimensional Keller¨CSegel system

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• 作者：Takayoshi Ogawa and Senjo Shimizu
• 关键词：Mathematics Subject Classification (2000) Primary 35K15 ; 46B70 ; Secondary 35K57 ; 42B25
• 刊名：Mathematische Zeitschrift
• 出版年：2010
• 出版时间：March, 2010
• 年：2010
• 卷：264
• 期：3
• 页码：601-628
• 全文大小：367.5 KB

文摘

We prove the maximal L ρ regularity of the Cauchy problem of the heat equation in the Besov space [(B)\dot]_1,r0(\mathbbRn){\dot{B}_{1,\rho}^0(\mathbb{R}^n)}, 1 < ρ ≤ ∞, which is not UMD space. And as its application, we establish the time local well-posedness of the solution of two dimensional nonlinear parabolic system with the Poisson equation in [(B)\dot]_1,20(\mathbbR2){\dot{B}_{1,2}^0(\mathbb{R}^2)} , where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined from the initial time. The small data global existence is also obtained in the same class.