On the Sharp Time Decay Rates for the 2D Generalized Quasi-geostrophic Equation and the Boussinesq System

被引：5

作者：

Stefanov, Atanas G. ^{[1
]}

Hadadifard, Fazel ^{[1
]}

机构：

[1] Univ Kansas, Dept Math, 1460 Jayhawk Blvd, Lawrence, KS 66045 USA

来源：

JOURNAL OF NONLINEAR SCIENCE | 2019年 / 29卷 / 05期

基金：

美国国家科学基金会;

关键词：

Time decay; Quasi-geostrophic equation; Boussinesq system; GLOBAL WELL-POSEDNESS; NAVIER-STOKES; VORTICITY EQUATIONS; ASYMPTOTIC-BEHAVIOR; WEAK SOLUTIONS; REGULARITY;

D O I：

10.1007/s00332-019-09543-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We compute the sharp time decay rates of the solutions of the IVP for quasi-geostrophic equation and the Boussinesq model, subject to fractional dissipation. Moreover, we explicitly identify the asymptotic profiles, the kernel of the alpha stable processes, which are analogues of the Oseen vortices.

引用

页码：2231 / 2296

页数：66

共 24 条

[1] On the global well-posedness for Boussinesq system
Abidi, H.
Hmidi, T.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 233 (01) : 199 - 220
[2] [Anonymous], 2012, PEKING U SUMMER SCH
[3] GLOBAL-SOLUTIONS OF 2-DIMENSIONAL NAVIER-STOKES AND EULER EQUATIONS
BENARTZI, M
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1994, 128 (04) : 329 - 358
[4] LARGE TIME DECAY AND GROWTH FOR SOLUTIONS OF A VISCOUS BOUSSINESQ SYSTEM
Brandolese, Lorenzo
Schonbek, Maria E.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 364 (10) : 5057 - 5090
[5] ASYMPTOTIC-BEHAVIOR FOR THE VORTICITY EQUATIONS IN DIMENSIONS 2 AND 3
CARPIO, A
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1994, 19 (5-6) : 827 - 872
[6] Global regularity for the 2D Boussinesq equations with partial viscosity terms
Chae, Dongho
[J]. ADVANCES IN MATHEMATICS, 2006, 203 (02) : 497 - 513
[7] Quasi-geostrophic equations, nonlinear Bernstein inequalities and α-stable processes
Chamorro, Diego
Lemarie-Rieusset, Pierre Gilles
[J]. REVISTA MATEMATICA IBEROAMERICANA, 2012, 28 (04) : 1109 - 1122
[8] Behavior of solutions of 2D quasi-geostrophic equations
Constantin, P
Wu, JH
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1999, 30 (05) : 937 - 948
[9] A maximum principle applied to quasi-geostrophic equations
Córdoba, A
Córdoba, D
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 249 (03) : 511 - 528
[10] Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R2
Gallay, T
Wayne, CE
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 163 (03) : 209 - 258

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