论文标题
BousSinesQ方程的零粘度极限，具有垂直粘度和半平面的Navier边界
Zero-viscosity Limit for Boussinesq Equations with Vertical Viscosity and Navier Boundary in the Half Plane
论文作者
论文摘要
在本文中，我们研究了具有垂直粘度和零扩散率的零粘度极限为$ 2 $ -D Boussinesq方程，这是一种非线性系统，在大气科学和海洋循环中产生了部分耗散。该域被视为带有Navier-Type边界的$ \ Mathbb {R} _+^2 $。我们证明了由边界sobolev空间中边界层扩展构建的近似解的非线性稳定性。本文还确定了无粘性极限的膨胀顺序和融合率。我们的论文扩展了BousSinesQ系统的部分零脱离限制结果，并由Chae D的完全耗散。数学。 203，不。 2，2006] $在整个案例中，在半平面上有部分耗散和纳维尔边界。
In this paper we study the zero-viscosity limit of $2$-D Boussinesq equations with vertical viscosity and zero diffusivity, which is a nonlinear system with partial dissipation arising in atmospheric sciences and oceanic circulation. The domain is taken as $\mathbb{R}_+^2$ with Navier-type boundary. We prove the nonlinear stability of the approximate solution constructed by boundary layer expansion in conormal Sobolev space. The expansion order and convergence rates for the inviscid limit are also identified in this paper. Our paper extends a partial zero-dissipation limit results of Boussinesq system with full dissipation by Chae D. $[Adv. Math. 203, no. 2, 2006]$ in the whole space to the case with partial dissipation and Navier boundary in the half plane.
