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 ρ and the velocity field u in R3. We assume that ρ0 is a small perturbation of 1 and (1−1/ρ0,u0) are analytic in Besov spaces with analyticity radius ω>0. We show that the corresponding solutions are analytic globally in time when (1−1/ρ0,u0) are sufficiently small. To do this, we introduce the exponential operator e(ω−θ(t))D acting on (1−1/ρ,u), where D is the differential operator whose Fourier symbol is given by |ξ|1=|ξ1|+|ξ2|+|ξ3| and θ(t) is chosen to satisfy θ(t)<ω globally in time.