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SUMMARY:On a generalization of the  Bardos-Tartar conjecture for nonlinear
  dissipative PDEs - Edriss Titi (University of Cambridge)
DTSTART:20240614T083000Z
DTEND:20240614T092000Z
UID:TALK214771@talks.cam.ac.uk
DESCRIPTION:In this talk I will show that every solution of a KdV-Burgers-
 Sivashinsky type equation blows up in the energy space\, backward in time\
 , provided the solution does not belong to the global attractor. This is a
  phenomenon contrast to the backward behavior of the 2D Navier-Stokes equa
 tions\, subject to periodic boundary condition\, studied by Constantin\, F
 oias\, Kukavica and Majda\, but analogous to the backward behavior of the 
 Kuramoto-Sivashinsky equation discovered by Kukavica and Malcok. I will al
 so discuss &nbsp\;the backward behavior of solutions to the damped driven 
 nonlinear Schroedinger equation\, the complex Ginzburg-Landau equation\, a
 nd the hyperviscous Navier-Stokes equations. In addition\, I will provide 
 some physical interpretation of various backward behaviors of several pert
 urbations of the KdV equation by studying explicit cnoidal wave solutions.
  Furthermore\, I will discuss the connection between the backward behavior
  and the energy spectra of the solutions. The study of &nbsp\;backward beh
 avior of dissipative evolution equations is motivated by a conjecture of &
 nbsp\;Bardos and Tartar which states that the solution operator of the two
 -dimensional Navier-Stokes equations maps the phase space into a dense sub
 set in this space.
LOCATION:Seminar Room 1\, Newton Institute
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