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

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 $H^{3/4}$.

References in corpus (2)

• On Two-dimensional Hamiltonian Transport Equations with $L_{loc}^p$ coefficients
• On Liouville transport equation with a force field in $B{V}_{loc}$

Cited by in corpus (2)

• Lagrangian flows for vector fields with gradient given by a singular integral
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