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.
|Original language||English (US)|
|Number of pages||28|
|Journal||Archive for Rational Mechanics and Analysis|
|State||Published - Jun 2008|
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)
- Mechanical Engineering