Analysis Seminar

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Singular solutions of the binormal flow

Speaker: Valeria Banica, LJLL - Sorbonne Université

Location: Online

Date: Thursday, March 11, 2021, 11 a.m.

Synopsis:

The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. This flow is also related to the classical continuous Heisenberg model in ferromagnetism and to the 1-D cubic Schrödinger equation. In this lecture I will first talk about the state of the art of the binormal flow conjecture, as well as about mathematical methods and results for the binormal flow. Then I will introduce a class of solutions at the critical level of regularity that generate singularities in finite time and describe some of their properties. These results are joint work with Luis Vega.

Notes:

Talk will be online via Zoom.