Asymptotic properties of the Boussinesq equations with Dirichlet boundary conditions
Asymptotic properties of the Boussinesq equations with Dirichlet boundary conditions
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DOI：
10.3934/dcds.2023040
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发表时间：
2021-09
影响因子：
1.1
通讯作者：
I. Kukavica;David Massatt;M. Ziane
中科院分区：
文献类型：
--
作者：
I. Kukavica;David Massatt;M. Ziane
我们解决的渐近性质的Boussinesq方程消失的热扩散率在一个有界区域与无滑移边界条件。我们证明了速度及其梯度的L^2范数的耗散性、Au的L^2范数的收敛性以及$\Vert A^{3/2}u\Vert_{L^2}$的$o（1）$型指数增长。我们还得到，在该区域的内部的涡度的梯度是有界的多项式函数的时间。
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 $\Vert A^{3/2}u\Vert_{L^2}$. We also obtain that in the interior of the domain the gradient of the vorticity is bounded by a polynomial function of time.