The characteristic Cauchy problem for Dirac fields on curved backgrounds
Langue
en
Document de travail - Pré-publication
Résumé en anglais
On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood ...Lire la suite >
On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in $L^2$ and we give an explicit definition of the space of data on the light-cone producing a solution in $H^1$. The method is based on energy estimates following L. Hörmander.< Réduire
Mots clés en espagnol
Goursat problem
Dirac equation
Lorentzian geometry
Regularity
Energy estimates
Project ANR
Equations hyperboliques dans des espaces-temps de la relativité générale : diffusion et résonances. - ANR-05-JCJC-0087
Origine
Importé de halUnités de recherche