Analyticity of solutions to the barotropic compressible Navier-Stokes equations

Abstract

In this paper, we establish analyticity of solutions to the barotropic compressible Navier-Stokes equations describing the motion of the density rho and the velocity field u in R-3. We assume that rho(0) is a small perturbation of 1 and (1 - 1/rho(0), u(0)) are analytic in Besov spaces with analyticity radius omega > 0. We show that the corresponding solutions are analytic globally in time when (1 - 1/rho(0), u(0)) are sufficiently small. To do this, we introduce the exponential operator e((omega-theta(t))D) acting on (1 - 1/rho, u), where D is the differential operator whose Fourier symbol is given by vertical bar xi vertical bar(1)=vertical bar xi(1)vertical bar + vertical bar xi(2)vertical bar + vertical bar xi(3)vertical bar and theta(t) is chosen to satisfy theta(t) < omega globally in time. (C) 2020 Elsevier Inc. All rights reserved.