Global Solutions for Incompressible Viscoelastic Fluids
- First Online:
- Cite this article as:
- lei, Z., Liu, C. & Zhou, Y. Arch Rational Mech Anal (2008) 188: 371. doi:10.1007/s00205-007-0089-x
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.