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
收藏
页码：393 / 410
页数：18
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