Archive for Rational Mechanics and Analysis

, Volume 188, Issue 3, pp 371–398

Global Solutions for Incompressible Viscoelastic Fluids

Article

DOI: 10.1007/s00205-007-0089-x

Cite this article as:
lei, Z., Liu, C. & Zhou, Y. Arch Rational Mech Anal (2008) 188: 371. doi:10.1007/s00205-007-0089-x

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.

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsNortheast Normal UniversityChangchunPeople’s Republic of China
  3. 3.Department of MathematicsPennsylvania State UniversityState collegeUSA
  4. 4.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  5. 5.Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of EducationShanghaiPeople’s Republic of China