96-6 Peter Constantin, Jiahong Wu

The Inviscid Limit for Non-Smooth Vorticity (29K, Latex) Jan 10, 96

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Abstract. We consider the inviscid limit of the incompressible Navier-Stokes equations for the case of two-dimensional non-smooth initial vorticities in Besov spaces. We obtain uniform rates of $L^p$ convergence of vorticities of solutions of the Navier Stokes equations to appropriately mollified solutions of Euler equations. We apply these results to prove strong convergence in $L^p$ of vorticities of Navier-Stokes solutions to vorticities of the corresponding, not mollified, Euler solutions. The short time results we obtain are for a class of solutions that includes vortex patches with rough boundaries and the long time results for a class of solutions that includes vortex patches with smooth boundaries.

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