کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4592540 | 1335109 | 2009 | 28 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: On a parabolic logarithmic Sobolev inequality On a parabolic logarithmic Sobolev inequality](/preview/png/4592540.png)
In order to extend the blow-up criterion of solutions to the Euler equations, Kozono and Taniuchi [H. Kozono, Y. Taniuchi, Limiting case of the Sobolev inequality in BMO, with application to the Euler equations, Comm. Math. Phys. 214 (2000) 191–200] have proved a logarithmic Sobolev inequality by means of isotropic (elliptic) BMO norm. In this paper, we show a parabolic version of the Kozono–Taniuchi inequality by means of anisotropic (parabolic) BMO norm. More precisely we give an upper bound for the L∞ norm of a function in terms of its parabolic BMO norm, up to a logarithmic correction involving its norm in some Sobolev space. As an application, we also explain how to apply this inequality in order to establish a long-time existence result for a class of nonlinear parabolic problems.
Journal: Journal of Functional Analysis - Volume 257, Issue 3, 1 August 2009, Pages 903-930