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.
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页码：3749 / 3765
页数：17
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