Uniform stability and convergence of the iterative solutions of the 3D steady viscous primitive equations of the ocean under the small depth assumption. (English) Zbl 1504.35568
Summary: 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 \(( \nu_1, \mu_1, \nu_2, \mu_2, \sigma, \gamma)\) of the Stokes, Newton and Oseen iterative solutions \((( \mathbf{u}^n, \theta^n), p^n)\) for the 3D steady PEs of the ocean under the small depth assumption and the uniqueness condition.
MSC:
| 35Q86 | PDEs in connection with geophysics |
| 35Q35 | PDEs in connection with fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 76U60 | Geophysical flows |
| 76D50 | Stratification effects in viscous fluids |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
primitive equations of ocean; uniqueness condition; Stokes iterative; Newton iterative; Oseen iterative; uniform convergenceReferences:
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