Local strong solutions to a compressible non‐Newtonian fluid with density‐dependent viscosity

Abstract

We consider the initial boundary problem for a compressible non‐Newtonian fluid with density‐dependent viscosity. The local existence of strong solution is established that is based on some compatibility condition. Moreover, it is also proved that the solutions are to blow up, and the maximum norm of velocity gradients controls the possible break down of the strong solutions. Copyright © 2016 John Wiley & Sons, Ltd.

Zero dissipation limit to rarefaction wave with vacuum for a one-dimensional compressible non-Newtonian fluid

“…Yuan and his cooperators obtained the existence result on the local strong solutions of initial-boundary-value problem in one dimensional non-Newtonian fluids see [28,29] and the references therein. Later Fang and Guo [5] gave the blowup criterion for the local strong solutions obtained in [28], constructed an analytical solutions to a class of compressible non-Newtonian fluids in [4], and considered the initial boundary problem for a compressible non-Newtonian fluid with densitydependent viscosity [6]. For more related results, we refer the reader to [3,27] and the references therein.…”