French-Japanese one day meeting in Tours

French-Japanese one day meeting in Tours

Date :  Thursday 31 of August  2023.

Place : This meeting will take place at the University of Tours on the campus « Parc Grandmont » bat E1, room E2290.

Presentation: This meeting will mainly focus on nonlinear dispersive equations with   deterministic or random approaches.

Program :

9h30-9h45Welcome coffee 
9h45-10h30Kotaro Tsugawa (Chuo University)
Local well-posedness of derivative Schrodinger equations on the torus
10h35-11h20Philippe Gravejat (Cergy University)Stability of the Ginzburg-Landau vortex
11h25-12h15Tomoyuki Tanaka  (Doshisha University)Local well-posedness for derivative nonlinear Schrödinger type equations with nonvanishing boundary conditions
14h00-14h50Luc Molinet (Tours University)On the LWP for the KP-I equation
14h55-15h45Takamori Kato (Saga University)Unconditional well-posedness in energy space for third order Benjamin-Ono equations on the torus
15h45-16h15Coffee and discussions … 


Stability of the Ginzburg-Landau vortex : We describe the proof of the orbital stability along the flow of the Gross-Pitaevskii equation of the vortex solution (of degree one) for the Ginzburg-Landau equation. This proof is based on the introduction of a functional framework taylored to investigate the minimality and stability properties of this vortex solution. We prove that a renormalized Ginzburg-Landau energy is well-defined in that framework and that the vortex solution is its unique global minimizer up to the invariances by translation and phase shift. We next derive a nonlinear coercivity estimate for this renormalized energy, which eventually leads to the proof of its orbital stability. This is a joint work with Eliot Pacherie (New York University at Abu Dhabi) and Didier Smets (Sorbonne University).