Analysis Seminar

We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow boundary in the zero-viscosity limit. We show that in a general setting, the energy dissipation rate is proportional to U¯V¯2 , where U¯ is the strength of the suction and V¯ is the tangential component of the difference between Euler and Navier-Stokes on the outflow boundary. Moreover, we show that the enstrophy within a layer of order ν/U¯ is comparable with the total enstrophy. The rate of enstrophy production near the boundary is inversely proportional to ν . This is based on joint work with Vincent Martinez, Anna Mazzucato, and Alexis Vasseur.