Abstract:
In a short note in 1984 T. Kato established a criterion for the vanishing viscosity limit to hold in the presence of boundaries, namely that the energy
dissipation must vanish in a small region near the boundary, as viscosity tends to zero. The proof is based on the use of a boundary corrector and energy estimates. In this talk, we will discuss Kato's result and its relation to
the physical phenomenon of the boundary layer. We then describe the application of these boundary correctors to several different scenarios involving boundary layers, including small obstacles, large domains, Euler-alpha and second grade fluids. |