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Dispersive effects of the incompressible viscoelastic fluids

  • * Corresponding author: Ruizhao Zi

    * Corresponding author: Ruizhao Zi
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  • 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.

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


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