1. Global well-posedness for the compressible Navier-Stokes equations with the highly oscillating initial velocity
- Author
-
Changxing Miao, Qionglei Chen, and Zhifei Zhang
- Subjects
Convection ,Well-posed problem ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,Stable equilibrium ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Hyperbolic systems ,Physics::Fluid Dynamics ,35Q30, 35B35 ,Parabolic system ,Mathematics - Analysis of PDEs ,Compressibility ,FOS: Mathematics ,Compressible navier stokes equations ,Well posedness ,Mathematical Physics ,Mathematics ,Analysis of PDEs (math.AP) - Abstract
Cannone \cite{Cannone} proved the global well-posedness of the incompressible Navier-Stokes equations for a class of highly oscillating data. In this paper, we prove the global well-posedness for the compressible Navier-Stokes equations in the critical functional framework with the initial data close to a stable equilibrium. Especially, this result allows us to construct global solutions for the highly oscillating initial velocity. The proof relies on a new estimate for the hyperbolic/parabolic system with convection terms., Comment: 43pages
- Published
- 2009
- Full Text
- View/download PDF