Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum

Abstract

In this article, we investigate an initial and boundary value problem for a class of compressible non-Newtonian fluids, provided the initial energy is small and the initial density containing the vacuum state is allowed. For $p>2$, we obtain the existence and uniqueness of the global strong solution for this problem in a one-dimensional bounded interval.

Keywords

• Non-Newtonian fluid
• Global strong solution
• A priori estimate
• Existence and uniqueness
• Vacuum