ASYMPTOTIC PROPERTIES OF THE BOUSSINESQ EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

被引：5

作者：

Kukavica, Igor ^{[1
]}

Massatt, David ^{[1
]}

Ziane, Mohammed ^{[1
]}

机构：

[1] Univ Southern Calif, Los Angeles, CA 90007 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2023年 / 43卷 / 08期

关键词：

Dimension theory; Poincare recurrences; multifractal analysis; discretetime model; singular Hopf bifurcation; GLOBAL WELL-POSEDNESS; LONG-TIME BEHAVIOR; REGULARITY; SYSTEM; PERSISTENCE;

D O I：

10.3934/dcds.2023040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We address the asymptotic properties for the Boussinesq equations with vanishing thermal diffusivity in a bounded domain with no-slip boundary conditions. We show the dissipation of the L-2 norm of the velocity and its gradient, convergence of the L-2 norm of Au, and an o(1)-type exponential growth for ||A(3/2)u||(L2). We also obtain that in the interior of the domain the gradient of the vorticity is bounded by a polynomial function of time.

引用

页码：3060 / 3081

页数：22

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