Prof. Dr. Eduard Feireisl - On Solvability of Certain Problems in Fluid Mechanics Involving Inviscid Fluids
Institute of Mathematics, Academy of Sciences of the Czech Republic
We present a general method of ''construction'' of solutions to systems of partial differential equations describing the motion of inviscid fluids. The method is based on a variable coefficients version of the oscillatory lemma proved in the context of the incompressible Euler system by C.DeLellis and L.Szekelyhidi. Several specific examples of fluid systems including the Korteweg fluid models, quantum fluids, the Euler-Fourier system, the Savage-Hutter model will be presented. We also discuss suitable admissibility criteria to ensure well-posedness of these probelms.