Archive for Rational Mechanics and Analysis

, Volume 188, Issue 3, pp 371–398

Global Solutions for Incompressible Viscoelastic Fluids


    • School of Mathematical SciencesFudan University
    • School of Mathematics and StatisticsNortheast Normal University
  • Chun Liu
    • Department of MathematicsPennsylvania State University
  • Yi Zhou
    • School of Mathematical SciencesFudan University
    • Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education

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


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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© Springer-Verlag 2007