Dispersive effects of the incompressible viscoelastic fluids

Daoyuan Fang; Ting Zhang; Ruizhao Zi

doi:10.3934/dcds.2018233

Article Contents

2018, Volume 38, Issue 10: 5261-5295. Doi: 10.3934/dcds.2018233

This issue Previous Article Collision-avoiding in the singular Cucker-Smale model with nonlinear velocity couplings Next Article Stability analysis for a family of degenerate semilinear parabolic problems

Dispersive effects of the incompressible viscoelastic fluids

1.
Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2.
School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China

* Corresponding author: Ruizhao Zi
* Corresponding author: Ruizhao Zi

Received: February 28, 2018

Published: September 2018

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Abstract

We consider the Cauchy problem of the $N$ -dimensional incompressible viscoelastic fluids with $N≥2$ . It is shown that, in the low frequency part, this system possesses some dispersive properties derived from the one parameter group $e^{± it\Lambda}$ . Based on this dispersive effect, we construct global solutions with large initial velocity concentrating on the low frequency part. Such kind of solution has never been seen before in the literature even for the classical incompressible Navier-Stokes equations.

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Mathematics Subject Classification: Primary: 76A10, 76D03.

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