Semiflow selection for the compressible Euler system

Abstract: Using the methods of the theory of Markov semigroups, we show the existence of a Borel measurable solution semiflow for the isentropic Euler system in the multidimensional setting. Solutions are understood as time dependent trajectories of the basic state variables -the mass density, the linear momentum, and the energy - in a suitable phase space. The underlying system of PDE's is satisfied in a generalized sense. The solution semiflow enjoys the standard semigroup properties and the solutions coincide with the strong solutionsof the isentropic Euler system as long as the latter exists. Moreover, they minimize the energy (maximize the energy dissipation) among all generalized solutions.

This is a joint work with D.Breit and M.Hofmanova.