A well-posedness result for the cubic NLS with irregular initial data.

par Marco Bravin

mardi 1 févr. 2022, 14:45 → 15:30 Europe/Paris

Fokko du Cloux (Bâtiment Braconnier, Université Lyon 1)

The vortex filament equation (VFE) is a geometric equation that describes the evolution of a curve of vorticity in a three dimensional incompressible inviscid fluid. Through the Hasimoto transformation, the VFE is associated with the cubic NLS equation. In this talk I will focus my attention on vortex filaments that are initially polygonal lines, which correspond to studying the cubic NLS with sum of delta of Dirac as initial data. In particular I will show local and large in time well-posedness for sufficiently small initial data in appropriated spaces. This is a joint work with Luis Vega.