Large time behavior of solutions to the inviscid liquid‐gas two‐phase flow model

Abstract

The purpose of this paper is to gain some insight into the existence theory and large time behavior of the inviscid liquid-gas two-phase flow model in R 3 . Main focus is on the influences of the damping on the qualitative behavior of solutions of the corresponding Cauchy problem under only the smallness assumption on H 3 -norm of the initial perturbation. The energy method combined with the low frequency and high frequency decomposition is used to obtain the desired decay of the solution and hence global existence. As a byproduct, L 2 -L 2 decay rates are obtained for the solution and its derivatives. This result implies that the friction effect of the damping contributes to enhance the decay rate of the velocity, even if there is no the additional L p -norm boundedness condition of the initial perturbation.