Global solution of 3D irrotational flow for gas dynamics in thermal nonequilibrium

Abstract

We study the three-dimensional irrotational flow for gas dynamics in thermal nonequilibrium. The global existence and large time behavior of the classical solution to the Cauchy problem are established when the initial data are near the equilibrium state with an additional $L^1$-norm bound. We mention that the uniform bound on derivatives of the entropy is obtained by using the a priori decay-in-time estimate on the velocity.