University of Connecticut/University of TexasSan Antonio

Tue 1 Dec 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012

Saddle Solutions of AllenCahn Equation on the Plane.

ESB2012
Tue 1 Dec 2015, 3:30pm4:30pm
Abstract
AllenCahn equation arises in the mathematical study of phase transition. Despite it's seemingly simple appearance, It has displayed very rich structure of solutions and involved with deep mathematics. In this talk, I will discuss the existence, symmetry and classification of saddle solutions of AllenCahn equation on the plane. In particular, I will describe the variational characterization of these solutions as a mountain pass solutions.
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University of Toronto

Tue 5 Jan 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012

Vortex filaments in the Euler equation

ESB2012
Tue 5 Jan 2016, 3:30pm4:30pm
Abstract
Abstract: Classical fluid dynamics arguments suggest that in certain
limits, the evolution of thin vortex filaments in an ideal incompressible
fluid should roughly be governed by an equation called the binormal
curvature flow. However, these classical arguments rely on assumptions
that are so unrealistic that it would be hard even to extract from them a
precise conjecture that admits any realistic possibility of a proof. We
present a different approach to this question that yields a reasonable
formulation of a conjecture and strong supporting evidence, and that
clarifies the very substantial obstacles to a full proof. Parts of the
talk are based on joint work with Didier Smets and with Christian Seis
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