Semiflow selection to models of general compressible viscous fluids

Abstract

We prove the existence of a semiflow selection with range the space of càglàd, i.e. left--continuous and having right--hand limits functions defined on $[0,\infty )$ and taking values in a Hilbert space. Afterwards, we apply this abstract result to the system arising from a compressible viscous fluid with a barotropic pressure of the type $a{\varrho }^{\gamma }$, $\gamma \ge 1$, with a viscous stress tensor being a nonlinear function of the symmetric velocity gradient.