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On the Euler+Prandtl expansion for the Navier-Stokes equations
PDE and Applied Math Seminar| Speaker: | Trinh Nguyen, USC |
| Location: | Zoom and MSB2112 https://ucdavis.zoom.us/j/97716142942 |
| Start time: | Thu, Oct 28 2021, 4:10PM |
I will talk about my recent work on the validity of the Euler+Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with Dirichlet boundary conditions in the vanishing viscosity limit, for initial vorticity that are analytic only near the boundary, and Sobolev smooth away from the boundary. Our work closes the gap between Sammartino-Caflisch results in 1998, which assume the analyticity of solutions on the entire half-plane, and Maekawa results in 2014, which assume that the initial vorticity identically zero near the boundary. Moreover, we are able to propagate the local analyticity for the Euler equation, which is a result of independent interest. This is a joint work with Igor Kukavica, Vlad Vicol and Fei Wang.