Uniform stability and convergence of the iterative solutions of the 3D steady viscous primitive equations of the ocean under the small depth assumption

Abstract

In this article, we design the Stokes, Newton and Oseen iterative methods of the 3D steady viscous primitive equations (PEs for brevity) of the ocean. Furthermore, we use some parameter dependent Sobolev norms to provide the uniform stability and convergence results with respect to the physical parameters (ν1,μ1,ν2,μ2,σ,γ) of the Stokes, Newton and Oseen iterative solutions ((un,θn),pn) for the 3D steady PEs of the ocean under the small depth assumption and the uniqueness condition.