Global solution and large-time behavior of the 3D compressible Euler equations with damping

Abstract

We construct the global unique solution to the compressible Euler equations with damping in R3. We assume the H3 norm of the initial data is small, but the higher order derivatives can be arbitrarily large. When the H˙−s norm (0⩽s<3/2) or B˙2,∞−s norm (0<s⩽3/2) of the initial data is finite, by a regularity interpolation trick, we prove the optimal decay rates of the solution. As an immediate byproduct, the Lp–L2(1⩽p⩽2) type of the decay rates follow without requiring that the Lp norm of initial data is small.