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 |
Keywords:
initial data with stratified vorticity; viscosity-independent estimates; vanishing viscosity; smooth vortex patches; Lipschitzian norm of velocity; inviscid limit; transport-diffusion equationReferences:
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