slideshow 3

Seminar on partial differential equations

Strong solutions to the steady compressible Navier-Stokes equations with inflow boundary conditions

Tomasz Piasecki
University of Warsaw

 

Tuesday, 2. October 2018 - 9:00 to 10:00

in IM, rear building, ground floor

We show the existence of strong solutions in Sobolev-Slobodetskii spaces to the stationary compressible Navier-Stokes equations with inflow boundary condition in a vicinity of given laminar solutions under the assumption that the pressure is a linear function of the density. In particular, we do not require any information on the gradient of the density or second gradient of the velocity. Our result holds provided certain condition on the shape of the boundary around the points where characteristics of the continuity equation are tangent to the boundary, which holds in particular for piecewise analytical boundaries.