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.
|9h45-10h30||Kotaro Tsugawa (Chuo University)||Local well-posedness of derivative Schrodinger equations on the torus|
|10h35-11h20||Philippe Gravejat (Cergy University)||Stability of the Ginzburg-Landau vortex|
|11h25-12h15||Tomoyuki Tanaka (Doshisha University)||Local well-posedness for derivative nonlinear Schrödinger type equations with nonvanishing boundary conditions|
|14h00-14h50||Luc Molinet (Tours University)||On the LWP for the KP-I equation|
|14h55-15h45||Takamori Kato (Saga University)||Unconditional well-posedness in energy space for third order Benjamin-Ono equations on the torus|
|15h45-16h15||Coffee 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).