LARGE-TIME REGULAR SOLUTIONS TO THE MODIFIED QUASI-GEOSTROPHIC EQUATION IN BESOV SPACES

被引：4

作者：

Tan, Wen ^{[1
]}

Dong, Bo-Qing ^{[1
]}

Chen, Zhi-Min ^{[1
]}

机构：

[1] Shenzhen Univ, Sch Math & Stat, Shenzhen 518052, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Modified quasi-geostrophic equations; Besov spaces; local well-posedness; smoothing effect; large-time global regular solutions; GLOBAL WELL-POSEDNESS; NAVIER-STOKES EQUATIONS; MAXIMUM-PRINCIPLES; INITIAL DATA; CRITERION;

D O I：

10.3934/dcds.2019152

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the study of the modified quasi-geostrophic equation partial derivative(t)theta + u . del theta + nu Lambda(alpha)theta = 0 with u = Lambda R-beta(perpendicular to)theta in R-2. By the Littlewood-Paley theory, we obtain the local well-posedness and the smoothing effect of the equation in critical Besov spaces. These results are applied to show the global existence of regular solutions for the critical case beta = alpha - 1 and the existence of regular solutions for large time t > T with respect to the supercritical case beta > alpha - 1 in Besov spaces. Earlier results for the equation in Hilbert spaces H-s spaces are improved.

引用

页码：3749 / 3765

页数：17

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