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Séminaire EDP, Modélisation et Calcul Scientifique (commun ICJ & UMPA)

Is dispersion a stabilizing or destabilizing mechanism? Landau-damping induced by fast background flows

by Edriss Titi (Texas A&M university)

mardi 22 mai 2018 de au (Europe/Paris)
at ICJ, UCBL - La Doua, Bât. Braconnier ( salle 112 )
Description
In this talk I will present a unified approach for the effect of fast rotation and dispersion as an averaging mechanism for, on the one hand, regularizing and stabilizing certain evolution equations, such as the Navier-Stokes and Burgers equations. On the other hand, I will  also present some results in which large dispersion acts as a destabilizing mechanism for the long-time dynamics of certain dissipative evolution equations, such as the Kuramoto-Sivashinsky equation. In addition, I will present some new results concerning two- and three-dimensional turbulent flows with high Reynolds numbers in periodic domains, which exhibit ``Landua-damping" mechanism due to large spatial average in the initial data.