Cauchy problem for non-autonomous Navier-Stokes equations in an unbounded domain

Abstract

This paper concerns the global existence of solutions to a system of non-linear compressible non-autonomous Navier–Stokes equations in an unbounded domain. To prove the global existence, we first study an approximate problem in a bounded domain and obtain a priori estimates independent of the boundary of the domain. Then letting the diameter of the domain tend to infinity, we get a global spherically symmetric solution as the limit.

Keywords:

• Navier–Stokes equations
• non-autonomous
• global existence

AMS Subject Classifications:

• 35Q35
• 35Q30
• 35L65
• 76N10

Disclosure statement

No potential conflict of interest was reported by the authors.