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

Nicolas Champagnat 1, * Pierre-Emmanuel Jabin 1, 2, *
* Corresponding author
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : 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 $H^{3/4}$.
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Nicolas Champagnat, Pierre-Emmanuel Jabin. Well-posedness in any dimension for Hamiltonian flows with non BV force terms. Communications in Partial Differential Equations, Taylor & Francis, 2010, 35 (5), pp.786-816. ⟨10.1080/03605301003646705⟩. ⟨inria-00373784v2⟩

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