Strong relaxation limit of multi-dimensional isentropic Euler equations

Abstract

This paper is devoted to study the strong relaxation limit of multi-dimensional isentropic Euler equations with relaxation. Motivated by the Maxwell iteration, we generalize the analysis of Yong (SIAM J Appl Math 64:1737–1748, 2004) and show that, as the relaxation time tends to zero, the density of a certain scaled isentropic Euler equations with relaxation strongly converges towards the smooth solution to the porous medium equation in the framework of Besov spaces with relatively lower regularity. The main analysis tool used is the Littlewood–Paley decomposition.