Tel. : (+33) 5 61 55
My work deals with the mathematical study of partial differential equations arising from physics with a strong emphasis on the qualitative description of the dynamics including singularity formation or long time asymptotics. I have mostly focused on canonical nonlinear dispersive, parabolic or kinetic models arising in various physical situations like nonlinear optics, plasma physics, fluid mechanics or astophysics. I am involved in three main thematic programs which have in commom the underlying problem: study the infinite dimensional flow near the solitary wave.
- Non linear Schrodinger equations: singularity formation for critical and super critical equations, stability and aysmptotic stability of soliton dynamcis, dynamical classification of solitary waves, long range models of Hartree type.
- Geometrical equations: study of energy critical/super critical problems, blow up for geometric equations like wave maps, Schrodinger maps or harmonic heat flow.
- Vlasov-Poisson system: nonlinear transport equations, stability and instability of steady states, singularity formation.
- Thematic program "Ondes nonlineaires et dispersion", April-July 2009, Institut Henri Poincare, Paris
- PDE's in Hammamet, Tunisia, Sept 2009
- Summer school on soliton dynamics, Santiago, Chile, July 2011