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.
Program :
| 9h30-9h45 | Welcome coffee | |
| 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 |
| 12h15-14h00 | Lunch | |
| 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 … |
Abstracts
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).