Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions

Zhen Lei

doi:10.3934/dcds.2014.34.2861

Article Contents

2014, Volume 34, Issue 7: 2861-2871. Doi: 10.3934/dcds.2014.34.2861

This issue Previous Article Curves of equiharmonic solutions, and problems at resonance Next Article Long-time behavior for a class of degenerate parabolic equations

Rotation-strain decomposition for the incompressible viscoelasticity in two dimensions

Zhen Lei^1,

1.
School of Mathematical Sciences, LMNS and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433

Received: March 31, 2013

Revised: July 31, 2013

Published: June 2014

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Abstract

In this paper, we revisit the 2D rotation-strain model which was derived in [14] for the motion of incompressible viscoelastic materials and prove its global well-posedness theory without making use of the equation of the rotation angle. The proof relies on a new identity satisfied by the strain matrix. The smallness assumptions are only imposed on the $H^2$ norm of initial velocity field and the initial strain matrix, which implies that the deformation tensor is allowed being away from the equilibrium of 2 in the maximum norm.

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Mathematics Subject Classification: Primary: 76D03, 76D09; Secondary: 35M10.

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