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Seminar in Analysis: Stefano Spirito

Stefano Spirito, University of L'Aquila

The vanishing viscosity problem for the Navier-Stokes equations in bounded domains

In this talk I will discuss the vanishing viscosity problem for the Navier-Stokes equations in a bounded domain. It is well-known that when Dirichlet conditions are imposed on the boundary the inviscid limit is currently an open and difficult problem. On the other hand when other type of boundary conditions are considered the situation became simpler. In this talk a particular type of Navier boundary conditions involving only the vorticity of the velocity field are considered. In particular, I will discuss recent results obtained in collaboration with Luigi Berselli (University of Pisa) concerning the inviscid limit in energy norm of the Leray weak solutions and the inviscid limit in higher norms of local smooth solutions of the Navier-Stokes equations.

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