Pusan National University and UBC

Tue 2 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105

Solitons for the mean curvature flow and inverse mean curvature flow

MATH 105
Tue 2 Oct 2018, 3:30pm4:30pm
Abstract
Selfsimilar solutions and translating solitons are not only special solutions of mean curvature flow (MCF) but a key role in the study of singularities of MCF. They have received a lot of attention. We introduce some examples of selfsimilar solutions and translating solitons for the mean curvature flow (MCF) and give rigidity results of some of them. We also investigate selfsimilar solutions and translating solitons to the inverse mean curvature flow (IMCF) in Euclidean space.
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MIT

Tue 9 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105

Minimal surfaces and the AllenCahn equation on 3 manifolds

MATH 105
Tue 9 Oct 2018, 3:30pm4:30pm
Abstract
The AllenCahn equation is a semilinear PDE that produces minimal surfaces via a certain singular limit. We will describe recent work proving index, multiplicity, and curvature estimates in the context of an AllenCahn minmax construction in a 3manifold. Our results imply, for example, that in a 3manifold with a generic metric, for every positive integer p, there is an embedded twosided minimal surface of Morse index p. This is joint with Otis Chodosh.
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UBC

Tue 23 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105

Global NavierStokes flows for nondecaying initial data with slowly decaying oscillation

MATH 105
Tue 23 Oct 2018, 3:30pm4:30pm
Abstract
We consider the Cauchy problem of 3D incompressible NavierStokes equations for uniformly locally square integrable initial data. The existence of a timeglobal weak solution has been known, when the square integral of the initial datum on a ball vanishes as the ball goes to infinity. For nondecaying data, however, the only known global solutions are either for perturbations of constants or when the velocity gradients are in Lp with finite p. In this talk, I will outline how to construct global weak solutions for general nondecaying initial data whose local oscillations slowly decay.
This is a joint work with TaiPeng Tsai.
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