Dispersive effect and global well-posedness of the compressible viscoelastic fluids

Abstract

This paper is concerned with the global well-posedness issue of the compressible viscoelastic fluids in the whole space RN,N≥2. The proof relies on the dispersive estimates to the linearized hyperbolic system combined with energy estimates to the hyperbolic-parabolic system. By exploiting the intrinsic structure of the system under some physical restrictions, we find that the compressible viscoelastic fluids admits a unique global solution with a class of large initial data in the sense of critical L2 framework.