Compressible Euler equation with damping on Torus in arbitrary dimensions

Nan Lu

Published 2013-09-19, updated 2014-10-19Version 3

We study the exponential stability of constant steady state of isentropic compressible Euler equation with damping on $\mathbb T^n$. The local existence of solutions is based on semigroup theory and some commutator estimates. We propose a new method instead of energy estimates to study the stability, which works equally well for any spatial dimensions.