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

共 35 条

[1]

[Anonymous], 1995, DYNAMICAL PROBLEMS N

[2] Global well-posedness of dissipative quasi-geostrophic equations in critical spaces [J].

Bae, Hantaek .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (01) :257-261

[3]

Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1

[4]

Caffarelli LA, 2010, ANN MATH, V171, P1903

[5] Global well-posedness in the super-critical dissipative quasi-geostrophic equations [J].

Chae, D ;

Lee, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 233 (02) :297-311

[6] A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation [J].

Chen, Qionglei ;

Miao, Changxing ;

Zhang, Zhifei .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 271 (03) :821-838

[7] Homogeneity Criterion for the Navier-Stokes Equations in the Whole Spaces [J].

Chen, Zhi Min ;

Xin, Zhouping .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2001, 3 (02) :152-182

[8] FORMATION OF STRONG FRONTS IN THE 2-D QUASI-GEOSTROPHIC THERMAL ACTIVE SCALAR [J].

CONSTANTIN, P ;

MAJDA, AJ ;

TABAK, E .

NONLINEARITY, 1994, 7 (06) :1495-1533

[9] Behavior of solutions of 2D quasi-geostrophic equations [J].

Constantin, P ;

Wu, JH .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1999, 30 (05) :937-948

[10] Nonlinear maximum principles for dissipative linear nonlocal operators and applications [J].

Constantin, Peter ;

Vicol, Vlad .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2012, 22 (05) :1289-1321

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