On fundamental solutions for non-local parabolic equations with divergence free drift

被引：21

作者：

Maekawa, Yasunori ^{[1
]}

Miura, Hideyuki ^{[2
]}

机构：

[1] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan

[2] Osaka Univ, Dept Math, Grad Sch Sci, Toyonaka, Osaka 5600043, Japan

来源：

ADVANCES IN MATHEMATICS | 2013年 / 247卷

关键词：

Non-local parabolic equations; Divergence free drift; Fundamental solutions; Nash iteration; 2D dissipative quasi-geostrophic equations; QUASI-GEOSTROPHIC EQUATION; SYMMETRIC JUMP-PROCESSES; DIRICHLET FORMS; DIFFUSION-EQUATIONS; UPPER-BOUNDS; CONTINUITY; OPERATORS; KERNELS;

D O I：

10.1016/j.aim.2013.07.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We are concerned with non-local parabolic equations in the presence of a divergence free drift term. By using the classical Nash approach, we show the existence of fundamental solutions together with continuity estimates, under weak regularity assumptions on the kernel of the non-local term and the velocity of the drift term. As an application, we give an alternative proof of global regularity for the two-dimensional dissipative quasi-geostrophic equations in the critical case. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：123 / 191

页数：69

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