RG Analysis and Partial Differential Equations

Graduate seminar on Advanced topics in PDE

Organizers

Schedule

This seminar takes place regularly on Fridays, at 14:15. The seminar will take place in person in SR 0.011. Please join the pdg-l mailing list for further information.

March 28 - Tetsu Mizumachi (Hiroshima)

Title: On transverse stability of line solitary waves for 2D long wave models

Abstract:

In this talk, I will explain modulations of 1-solitons of the KP-II equation and how the idea works for elastic 2-line solitons or resonant solitons. I will also mention transverse stability of line solitary waves for the Benney-Luke equation and the 2D-Toda equation.

April 11 - Nikolay Tzvetkov (Lyon)

Title: Probabilistic well-posedness for the nonlinear Schrödinger equation on the two dimensional sphere

Abstract:

It is known that the minimal Sobolev regularity needed for the semi-linear, local well-posedness of the non linear Schrödinger equation, posed on a two dimensional domain depends heavily on the geometry of the domain. In this talk we will observe a similar phenomenon in the study of the probabilistic well-posedness. This is a joint work with Burq-Camps-Sun.

April 18 - easter friday

April 25 - Fred Lin (Bonn)

Title: On a smoothing inequality related to triangular Hilbert transform along general curve

Abstract:

A kind of smoothing inequality plays a central role in proving the boundedness of the triangular Hilbert transform along curve, its maximal variant and the associated Roth type problem. I will survey the recent developement in this field, then sketch the proof of such smoothing inequality. This is joint work with Martin Hsu.