Global Solutions for Incompressible Viscoelastic Fluids

Details Global Solutions for Incompressible Viscoelastic Fluids Global Solutions for Incompressible Viscoelastic Fluids

2009-01-23

arxiv.org/abs/0901.3658v1

Arch. Ration. Mech. Anal., 188 (2008), no. 3, 371--398

Mathematics

Analysis of PDEs

We prove the existence of global smooth solutions to the Cauchy problem for the incompressible viscoelastic system of Oldroyd-

Scientific paper

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.

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