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Viscous vortex patches. (Poches de tourbillon visqueuses.) (French) Zbl 0903.76020

Summary: We investigate the inviscid limit for two-dimensional incompressible Navier-Stokes equations when the initial data have stratified vorticity (smooth vertex patches, for instance). Uniform estimates for transport-diffusion equation yield independent of the viscosity estimates for the Lipschitzian norm of the velocity. This provides the strong convergence for solutions with stratified vorticity (thus for vortex patches) when viscosity tends to \(0\).

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
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