Applied math seminar
Title: Long-time dynamics of the sine-Gordon equation
Speaker: Gong Chen, Fields Institute
Date and time:
21 Oct 2020,
2:30pm -
3:20pm
Location: via Zoom
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Abstract: In the first part of this talk, I will illustrate how to compute the long-time asymptotics of the sine-Gordon equation using its integrable structure and nonlinear steepest descent. Then I will discuss the asymptotic stability of solitons of the sine-Gordon equation in weighted energy space. It is known that the obstruction to the asymptotic stability for the sine-Gordon equation in the energy space is the existence of small breathers which is also closely related to the emergence of wobbling kinks. Our stability analysis gives a criterion for the weight which is sharp up to the endpoint so that the asymptotic stability holds.
Please email the organizer
if you need the Zoom link.
Title: Desingularization of vortices and Leapfrogging phenomenon for Euler flows
Speaker: Jun-Cheng Wei, University of British Columbia
Date and time:
14 Oct 2020,
2:30pm -
3:20pm
Location: via Zoom
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Abstract: In 1858, Helmholtz predicted that two ring-formed filaments in
fluids will pass through each other and become leapfrogging. In this
talk I will give a rigorous justification of Helmholtz's conjecture for
3D Euler flow, and also discuss the dynamical desingularization of
vortices for 2D Euler flows. The key ingredients are new gluing methods
for Euler flows. (Joint work with Juan Davila, Manuel del Pino and
Monica Musso.)
Please contact the organizer if you need the Zoom link.
Title: Effect of the rotation on the Primitive Equations for planetary geophysical flows
Speaker: Slim Ibrahim, University of Victoria
Date and time:
23 Sep 2020,
2:30pm -
3:30pm
Location: via Zoom
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Large scale dynamics of the oceans and the atmosphere are commonly governed by the primitive equations (PEs), also known as Hydrostatic Euler Equations. It is well-known that the 3D viscous primitive equations are globally well-posed in Sobolev spaces. In this talk, first, I
will briefly discuss the ill-posedness in Sobolev spaces, the local well-posedness in the
space of analytic functions, and finite-time blowup of solution to the 3D inviscid PEs with rotation (Coriolis force). Moreover, I will also show, in the case
of “well-prepared” analytic initial data, the regularizing effect of the Coriolis force by providing a lower bound for the life-span of the solutions that grows toward infinity with the rotation rate. These are joint works with T. E. Ghoul (NYUAD), Quyuan Lin (Texas A&M) and Edriss S. Titi (Texas A&M and University of Cambridge).
