High-electric-field limit for the Vlasov–Maxwell–Fokker–Planck system
Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
Hyperbolic methods for Einstein's equations.
Integrability and Einstein's equations
1. Introduction. In recent years, there has been considerable interest in Oxford and elsewhere in the connections between Einstein's equations, the (anti-) self-dual Yang-Mills (SDYM) equations, and the theory of integrable systems. The common theme running through this work is that, to a greater or lesser extent, all three areas involve questions that can be addressed by twistor methods. In this paper, I shall review progress, with particular emphasis on the known and potential applications in...
Klein Paradox and Superradiance for the charged Klein-Gordon Field
La diffraction en métrique de Schwarzschild : complétude asymptotique et résonances
L’effet Hawking
Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method...
Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge.
Méthodes géométriques dans l’étude des équations d’Einstein
L’étude de l’équation des ondes et de ses perturbations a montré l’importance d’un certain nombre d’objets géométriques, tels que les cônes sortants et rentrants, les champs de Lorentz, des repères isotropes adaptés, etc. Parmi les systèmes d’équations hyperboliques non linéaires, les équations d’Einstein jouent un rôle central ; leur étude a nécessité, dans le cas d’un espace-temps courbe, la construction d’objets analogues à ceux du cas plat, cônes, repères adaptés, etc. La construction de ces...
Nonresonant smoothing for coupled wave + transport equations and the Vlasov-Maxwell system.
On classical solutions of the relativistic Vlasov-Klein-Gordon system.
On invariants of continuous subgroups of the generalized Poincaré group .
On Kato's inequality for the Weyl quantized relativistic Hamiltonian.
On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.
Opérateur de diffraction pour le système de Maxwell en métrique de Schwarzschild
Recursions of symmetry orbits and reduction without reduction.
Regularity and geometric properties of solutions of the Einstein-Vacuum equations
We review recent results concerning the study of rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. We develop new analytic methods based on Strichartz type inequalities which results in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of...
Remarks on relativistic Schrödinger operators and their extensions