Asymptotic stability of planar rarefaction wave to a multi-dimensional two-phase flow

Abstract

<p style='text-indent:20px;'>We are concerned with the time-asymptotic stability of planar rarefaction wave to a non-conservative two-phase flow system described by two-dimentional compressible Euler and Navier-Stokes equations through drag force. In this paper, we show the planar rarefaction wave to a non-conservative compressible two-phase model is asymptotically stable under small initial perturbation in <inline-formula><tex-math id="M1">\begin{document}$ H^3 $\end{document}</tex-math></inline-formula>. The main difficulties overcome in this paper come from the non-viscosity of one fluid and the interaction between two fluids caused by drag force. The stability result is proved by the energy method.</p>