Low Mach number limit for the degenerate Navier-Stokes equations in presence of strong stratification. (English) Zbl 1516.35331
Summary: In this paper, we investigate the low Mach and low Froude numbers limit for the compressible Navier-Stokes equations with degenerate, density-dependent, viscosity coefficient, in the strong stratification regime. We consider the case of a general pressure law with singular component close to vacuum, and general ill-prepared initial data. We perform our study in the three-dimensional periodic domain. We rigorously justify the convergence to the generalised anelastic approximation, which is used extensively to model atmospheric flows.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q86 | PDEs in connection with geophysics |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 86A10 | Meteorology and atmospheric physics |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35D30 | Weak solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
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