Global Existence of Classical Solutions for the Two-Dimensional Oldroyd Model via the Incompressible Limit

In this paper, we will study the Oldroyd model describing fluids with viscoelastic properties. Global classical solutions for the two-dimensional incompressible Oldroyd model with small initial displacements are shown to exist via the incompressible limit. The main difficulty is the lack of the damping mechanism on the deformation tensor.

[1]  D. Ebin,et al.  Global solutions of the equations of elastodynamics for incompressible materials , 1996 .

[2]  Thomas C. Sideris,et al.  On almost global existence for nonrelativistic wave equations in 3D , 1996 .

[3]  Sergiu Klainerman,et al.  Uniform decay estimates and the lorentz invariance of the classical wave equation , 1985 .

[4]  D. Ebin,et al.  Global solutions of the equations of elastodynamics of incompressible neo-Hookean materials. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Zhen Lei,et al.  Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit* , 2006 .

[6]  K. R. Rajagopal,et al.  Numerical simulations and global existence of solutions of two-dimensional flows of fluids with pressure- and shear-dependent viscosities , 2003, Math. Comput. Simul..

[7]  J. Lumley,et al.  Mechanics of non-Newtonian fluids , 1978 .

[8]  A. Majda,et al.  Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit , 1981 .

[9]  Serge Alinhac,et al.  Blowup for Nonlinear Hyperbolic Equations , 1995 .

[10]  Thomas C. Sideris.  Nonresonance and global existence of prestressed nonlinear elastic waves , 2000 .

[11]  Yoshihiro Shibata,et al.  Global existence and exponential stability of small solutions to nonlinear viscoelasticity , 1992 .

[12]  Thomas C. Sideris,et al.  GLOBAL EXISTENCE FOR 3D INCOMPRESSIBLE ISOTROPIC ELASTODYNAMICS VIA THE INCOMPRESSIBLE LIMIT , 2005 .