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

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 H2(R3) x H1(R3), we prove the global existence and regularity of strong solutions for the Navier-Stokes-Korteweg equations.

Automated summary

In this article, we investigate the three-dimensional compressible Navier-Stokes-Korteweg equations with the effect of external potential force. By assuming the smallness of both the external potential force and the initial perturbation, we prove the global existence and regularity of strong solutions for the Navier-Stokes-Korteweg equations.