Publication

Non-Uniqueness Of Integral Curves For Autonomous Hamiltonian Vector Fields

Massimo Sorella
2022
Journal Articles

Abstract

In this work we prove the existence of an autonomous Hamiltonian vector field in W-1,W-r(T-d; R-d) with r < d - 1 and d >= 4 for which the associated transport equation has non-unique positive solutions. As a consequence of Ambrosio's superposition principle [2], we show that this vector field has non-unique integral curves with a positive Lebesgue measure set of initial data and moreover, we show that the Hamiltonian is not constant along these integral curves.

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Non-Uniqueness Of Integral Curves For Autonomous Hamiltonian Vector Fields

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