Existence of global strong solutions for Navier–Stokes equations with external force

Abstract

We consider the initial boundary value problems (IBVPs) for 1D isentropic compressible Navier–Stokes equations with density-dependent viscosity coefficients and external force. If the initial data is regular, the existence and uniqueness of global strong solution to IBVP are proved in this article.

Keywords:

• Navier–Stokes equations
• strong solution
• external force

AMS Subject Classifications::

• 35Q35
• 76D03

Acknowledgements

The research of R.X. Lian is partially supported by the National Natural Science Foundation of China (No. 11101145, 10871134) and the Program for New Century Excellent Talents in University support of the Ministry of Education of China ♯ NCET-06-0186.