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

Mengni Li Yan-Lin Wang YMSC, Tsinghua University, Beijing, China

Analysis of PDEs mathscidoc:2204.03008

2022.2
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 R2+ 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 the 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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@inproceedings{mengni2022zero-viscosity,
  title={Zero-viscosity Limit for Boussinesq Equations with Vertical Viscosity and Navier Boundary in the Half Plane},
  author={Mengni Li, and Yan-Lin Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428132034041998136},
  year={2022},
}
Mengni Li, and Yan-Lin Wang. Zero-viscosity Limit for Boussinesq Equations with Vertical Viscosity and Navier Boundary in the Half Plane. 2022. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428132034041998136.
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