Rocky Mountain Journal of Mathematics

Global existence and decay rate of strong solution to incompressible Oldroyd type model equations

Baoquan Yuan and Yun Liu

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This paper investigates the global existence and the decay rate in time of a solution to the Cauchy problem for an incompressible Oldroyd model with a deformation tensor damping term. There are three major results. The first is the global existence of the solution for small initial data. Second, we derive the sharp time decay of the solution in $L^{2}$-norm. Finally, the sharp time decay of the solution of higher order Sobolev norms is obtained.

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Rocky Mountain J. Math., Volume 48, Number 5 (2018), 1703-1720.

First available in Project Euclid: 19 October 2018

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Zentralblatt MATH identifier

Primary: 35A01: Existence problems: global existence, local existence, non-existence 35Q35: PDEs in connection with fluid mechanics 76A10: Viscoelastic fluids

Incompressible Oldroyd model damping term global existence decay rate


Yuan, Baoquan; Liu, Yun. Global existence and decay rate of strong solution to incompressible Oldroyd type model equations. Rocky Mountain J. Math. 48 (2018), no. 5, 1703--1720. doi:10.1216/RMJ-2018-48-5-1703.

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