Existence and nonlinear stability of stationary solutions to the full compressible Navier-Stokes-Korteweg system

摘要

This paper is concerned with the existence, uniqueness, and nonlinear stability of stationary solutions to the Cauchy problem of the full compressible Navier-Stokes-Korteweg system effected by the given mass source, the external force of general form, and the energy source in R3. Based on the weighted L~2-method and some delicate L~∞ estimates on solutions to the linearized problem， the existence and uniqueness of stationary solution are obtained by the contraction mapping principle. The proof of the stability result is given by an elementary energy method and relies on some intrinsic properties of the full compressible Navier-Stokes-Korteweg system.