Solution semiflow to the isentropic Euler system

摘要: It is nowadays well understood that the multidimensional isentropic Euler system desperately ill--posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail ensure both global existence uniqueness. We propose a different approach well--posedness of this based on ideas from theory Markov semigroups: we show Borel measurable solution semiflow. To end, introduce notion dissipative which as time dependent trajectories basic state variables - mass density, linear momentum, energy in suitable phase space. The underlying PDEs satisfied generalized sense. semiflow enjoys standard semigroup property coincide with strong long latter exist. Moreover, they minimize (maximize dissipation) among solutions.