Global Solutions for Incompressible Viscoelastic Fluids

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...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis Vol. 188; no. 3; pp. 371 - 398
Main Authors: lei, Zhen, Liu, Chun, Zhou, Yi
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.06.2008
Springer
Springer Nature B.V
Subjects:
Classical Mechanics
Complex Systems
Exact sciences and technology
Fluid dynamics
Fluid- and Aerodynamics
Fundamental areas of phenomenology (including applications)
General theory
Magnetohydrodynamics and electrohydrodynamics
Mathematical and Computational Physics
Mathematical methods in physics
Numerical approximation and analysis
Ordinary and partial differential equations, boundary value problems
Physics
Physics and Astronomy
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Studies
Theoretical
Global Solution
Global Existence
Deformation Tensor
Strain Energy Function
Nonlinear Wave Equation
Viscoelastic fluid
Viscoelasticity
Magnetohydrodynamics
Tori
Oldroyd fluid
Fluid-structure interactions
Incompressible fluid
Liquid crystals
Liquid mixtures
Global solution
Global local method
Cauchy problem
ISSN:0003-9527, 1432-0673
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-007-0089-x