Well-posedness in any dimension for Hamiltonian flows with non BV force terms

Nicolas Champagnat (1) , Pierre-Emmanuel Jabin (1, 2)

1 TOSCA - Simuler et calibrer des modèles stochastiques
2 JAD - Laboratoire Jean Alexandre Dieudonné

We study existence and uniqueness for the classical dynamics of a particle in a force field in the phase space. Through an explicit control on the regularity of the trajectories, we show that this is well posed if the force belongs to the Sobolev space $H^{3/4}$.

Mots clés: flows for ordinary differential equations; kinetic equations; stability estimates

Domaines: Analyse classique [math.CA]

Nicolas Champagnat, Pierre-Emmanuel Jabin. Well-posedness in any dimension for Hamiltonian flows with non BV force terms. Communications in Partial Differential Equations, 2010, 35 (5), pp.786-816. ⟨10.1080/03605301003646705⟩. ⟨inria-00373784v2⟩