Zero-viscosity Limit for Boussinesq Equations with Vertical Viscosity and Navier Boundary in the Half Plane

arXiv2202.02712MaRDI QIDQ6507728

Mengni Li, Yan-Lin Wang

Abstract: 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 optimal 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.

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