Archive for Rational Mechanics and Analysis

, Volume 188, Issue 3, pp 371-398

First online:

Global Solutions for Incompressible Viscoelastic Fluids

  • Zhen leiAffiliated withSchool of Mathematical Sciences, Fudan UniversitySchool of Mathematics and Statistics, Northeast Normal University Email author 
  • , Chun LiuAffiliated withDepartment of Mathematics, Pennsylvania State University
  • , Yi ZhouAffiliated withSchool of Mathematical Sciences, Fudan UniversityKey Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education

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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.