, Volume 188, Issue 3, pp 371-398
Date: 03 Nov 2007

Global Solutions for Incompressible Viscoelastic Fluids

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Abstract

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near- equilibrium initial data. The results hold in both two- and three-dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals, and mixture problems.

Communicated by A. Bressan