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Zbl 0937.35124
Danchin, Raphaël
Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque. (Persistence of geometric structures and inviscid limit for incompressible fluids in any dimension.). (French)
[J] Bull. Soc. Math. Fr. 127, No.2, 179-227 (1999). ISSN 0037-9484

The author investigates the inviscid limit for $d$-dimensional incompressible Navier-Stokes equations. Supposing that the initial vorticity has striated regularity (which is a natural way of generalising the structure of vortex patches), he proves the persistence of striated regularity locally in time and uniformly with respect to the viscosity, together with uniform estimates on a fixed time interval for the Lipschitzian norm of the velocity. The author proves the strong convergence of the solution of Navier-Stokes equations to the solution of Euler equations with the same initial datum when viscosity tends to zero. In the last part of the paper he establishes a persistence and convergence result for the conormal regularity.
[A.Carabineanu (Bucureşti)]

MSC 2000:: *35Q30 Stokes and Navier-Stokes equations
76D17 Viscous vortex flows
76D03 Existence, uniqueness, and regularity theory
35B65 Smoothness of solutions of PDE

Keywords: vortex patch; viscid fluid; conormal regularity; nonviscid limit

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