On the global well-posedness the derivative nonlinear Schrödinger equation on the torus

Vortrag von Prof. Dr. Hajer Bahouri

Sprecher eingeladen von: Prof. Dr. Klaus Widmayer

Datum: 19.03.26  Zeit: 16.15 - 18.00  Raum: Y27H35/36

In this talk, I will present a recent joint work with Galina Perelman concerning the derivative nonlinear Schrödinger (DNLS) equation on the torus. The DNLS equation which is a canonical dispersive equation arising in a variety of physical contexts is known to be completely integrable (and then it admits a spectral formulation, an infinite number of conservation laws and explicit families of conservation laws). The main difficulty of this equation is the lack of coercivity of its conservation laws in the regime above the algebraic soliton threshold, and this makes large data global well-posedness a challenging issue. This equation was solved a short time ago on the real line, while  the case of the torus is still less understood. In this work, we prove  global well-posedness for DNLS equation on the torus.

The first part of my presentation will be devoted to a general overview of DNLS and completely integrable equations, then I will on the case of the torus  by providing the new arguments that enabled us to achieve our goal.