Pierre RAPHAEL

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Contact Universite Paul Sabatier Institut de Mathematiques de Toulouse Batiment 1R3, bureau 308 118 route de Narbonne F-31062 Toulouse Cedex 9 France Tel. : (+33) 5 61 55 76 59 e-mail: pierre.raphaelatmath.univ-toulouse.fr

Research interests

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.

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