Local existence and uniqueness of classical solutions for a compressible Oldroyd-B model with vacuum

Abstract

In this paper, we consider compressible Oldroyd-B equations in a bounded or unbounded domain Ω of $R^3$. Assuming that the initial data satisfy a natural compatibility condition, we show the local existence and uniqueness of the classical solutions for Oldroyd-B equations through some high-order estimations with respect to time weighting. To obtain the result, the initial density does not need to differ from zero and may vanish in an open subset (vacuum) of Ω or decay at infinity when Ω is unbounded.