Global Solutions for Incompressible Viscoelastic Fluids
Analysis of PDEs
2009-11-13 v1
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.
Keywords
Cite
@article{arxiv.0901.3658,
title = {Global Solutions for Incompressible Viscoelastic Fluids},
author = {Zhen Lei and Chun Liu and Yi Zhou},
journal= {arXiv preprint arXiv:0901.3658},
year = {2009}
}
Comments
We prove the existence of global smooth solutions to the Cauchy problem for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial data