Semiflow selection to models of general compressible viscous fluids

Abstract

We prove the existence of a semiflow selection with range the space of c\`agl\`ad, 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 $a\varrho^{\gamma}$, $\gamma \geq 1$, with a viscous stress tensor being a nonlinear function of the symmetric velocity gradient.