Existence of global weak solutions for a 3D Navier–Stokes–Poisson–Korteweg equations

Abstract

The purpose of this work is to study the global-in-time existence of weak solutions of a viscous capillary model of plasma expressed as a so-called Navier–Stokes–Poisson–Korteweg model for large data in three-dimensional space. Using the compactness argument, we prove the existence of global weak solutions in the classical sense to such system with a cold pressure.

Keywords:

• Navier–Stokes–Poisson–Korteweg equations
• global weak solutions
• cold pressure
• degenerate viscosity

AMS Subject Classifications:

• 35G25
• 35Q30
• 35Q40
• 35B40
• 76Y05

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

J. Yang’s research was partially supported by the Joint Funds of the National Natural Science Foundation of China [grant number U1204103].