Local existence of strong solution for a class of compressible non-Newtonian fluids with non-Newtonian potential

摘要

The aim of this paper is to discuss the existence and uniqueness of local solutions for a class of isentropic compressible non-Newtonian fluids with non-Newtonian potential in one-dimensional bounded intervals. The first difficult point in this paper is that we allow the initial vacuum; another one is that the viscosity term and Newtonian potential term are fully nonlinear, that is, the viscosity term adopts the O.A. Ladyzhenskaya model (p > 2); the potential term employs the q-Laplace form (1 < q < 2).