FAR-FIELD REGULARITY FOR THE SUPERCRITICAL QUASI-GEOSTROPHIC EQUATION

被引：0

作者：

Kukavica, Igor ^{[1
]}

Wang, Fei ^{[2
]}

机构：

[1] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA

[2] Univ Maryland, Dept Math, 4176 Campus Dr, College Pk, MD 20742 USA

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2018年 / 16卷 / 02期

关键词：

quasi-geostrophic equation; eventual regularity; supercritical; weighted decay; NAVIER-STOKES EQUATIONS; GLOBAL WELL-POSEDNESS; NONLINEAR SPECTRAL MANIFOLDS; WEAK SOLUTIONS; ASYMPTOTIC-BEHAVIOR; MAXIMUM-PRINCIPLES; L2; DECAY; FLOWS;

D O I：

10.4310/CMS.2018.v16.n2.a4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We address the far field regularity for solutions of the surface quasi-geostrophic equation thetat + u.del theta + A(2 alpha)theta = 0 u = R-inverted perpendicular&theta = (-R2theta,R1theta) in the supercritical range 0 < alpha < 1/2 with alpha sufficiently close to 1/2. We prove that if the datum is sufficiently regular, then the set of space-time singularities is compact in R-2 x R. The proof depends on a new spatial decay result on solutions in the supercritical range.

引用

页码：393 / 410

页数：18

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