Radius of analyticity of solutions to compressible Navier–Stokes–Korteweg system

Abstract

We study the analyticity and Gevrey regularity for the solutions to the compressible Navier–Stokes–Korteweg system. It was observed by Charve et al (2021 Indiana Univ. Math. J. 70 1903–44) that this system has the full parabolicity property due to the coupling of the equations given by the Korteweg capillarity term, which allows them to prove the analyticity of the solutions in the whole space with radius bounded from below by . In this paper, we improve this lower bound, motivated by the works of Chemin et al (2020 Math. Res. Lett. 27 1631–43) concerning the classical Navier–Stokes system. We also study the compressible Navier–Stokes–Korteweg system with periodic boundary condition and we show that the radius of analyticity for the mild solution is bounded from below by Ct.