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On 2D Viscoelasticity with Small Strain

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Abstract

An exact two-dimensional rotation–strain model describing the motion of Hookean incompressible viscoelastic materials is constructed by the polar decomposition of the deformation tensor. The global existence of classical solutions is proved under smallness assumptions only on the size of the initial strain tensor. The proof of global existence utilizes the weak dissipative mechanism of motion, which is revealed by passing the partial dissipation to the whole system.

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Authors and Affiliations

  1. Shanghai Key Laboratory for Contemporary Applied Mathematics, Key Laboratory of Nonlinear Mathematical Models and Methods of Ministry of Education, School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Zhen Lei

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  1. Zhen Lei
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Correspondence to Zhen Lei.

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Lei, Z. On 2D Viscoelasticity with Small Strain. Arch Rational Mech Anal 198, 13–37 (2010). https://doi.org/10.1007/s00205-010-0346-2

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  • DOI: https://doi.org/10.1007/s00205-010-0346-2

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