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

TL;DR

This paper establishes the existence and uniqueness of classical particle trajectories under Hamiltonian flows with forces in Sobolev space H^{3/4}, extending well-posedness results to any spatial dimension.

Contribution

It proves well-posedness for Hamiltonian flows with forces in H^{3/4} Sobolev space, even without BV regularity, in any dimension.

Findings

Existence and uniqueness of trajectories for forces in H^{3/4}.

Explicit regularity control of trajectories.

Extension of well-posedness to arbitrary dimensions.

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 $H^{3/4}$.