Two results on the inviscid limits of Navier-Stokes equations

Two results on the inviscid limits of Navier-Stokes equations

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Trinh Nguyen, Penn State University
Fine Hall 322

The inviscid limit of Navier-Stokes is one of the most fundamental and challenging problem in fluid dynamics. For domains with boundaries under no-slip boundary conditions, the problem is largely open due to large convection terms in the inviscid limit. On the whole space R2, the problem is open for less regular initial data, except for vortex patches and point vortices. In this talk, I will discuss two recent results on the inviscid limit of Navier-Stokes. The first result is justifying the inviscid limit on half-space, under no-slip boundary condition for analytic data, without doing the Prandtl asymptotic expansion. The second result is the inviscid limit on the whole space for vortex-wave data, which rigorously justifies the vortex-wave system derived in the early 90s by Marchioro-Pulvirenti as a vanishing viscosity limit of Navier-Stokes.