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Singularity formation in the generalized Benjamin-Ono equation
Rotating fluids in a cylinder
| 1. | LMC - IMAG, UMR 5523 (CNRS-UJF-INPG), B.P. 53, 38041 Grenoble Cedex 9, France |
| 2. | CEA/DIF, B.P. 12, 91680 Bruyères le Châtel, France |
| 3. | UMPA (CNRS UMR 128), E.N.S. Lyon, 46 allée d'Italie, 69364 Lyon cedex 07, France |
In a second section, we discuss the compressible Navier--Stokes equations with anisotropic viscosity tensor in the combined low Mach and low Rossby number limit. In the case of well prepared initial data, we prove that global weak solutions with Dirichlet boundary conditions converge to the solution of a two--dimensional quasi-geostrophic model taking into account the compressibility. In the case of ill prepared data, we only show that we can hope a strong convergence result under the same kind of assumptions as in the incompressible case.
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