Global existence of strong solutions to compressible Navier-Stokes-Korteweg equations with external potential force

Abstract

In this article, we consider a three dimensional compressible Navier-Stokes-Korteweg equations with the effect of external potential force. Under the smallness assumptions on both the external potential force and the initial perturbation of the stationary solution in $ H^2(\mathbb{R}^3)\times H^1(\mathbb{R}^3) $, we prove the global existence and regularity of strong solutions for the Navier-Stokes-Korteweg equations.

Keywords

• navier-stokes-korteweg equations
• stationary solution
• global existence