Compressible Euler equation with damping on Torus in arbitrary dimensions Nan Lu 35L04compressible euler 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. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5488 10.1512/iumj.2015.64.5488 en Indiana Univ. Math. J. 64 (2015) 343 - 356 state-of-the-art mathematics http://iumj.org/access/