Uniqueness of signed measures solving the continuity equation for Osgood vector fields

Details Uniqueness of signed measures solving the continuity equation for Osgood vector fields Uniqueness of signed measures solving the continuity equation for Osgood vector fields

2008-07-10

arxiv.org/abs/0807.1592v1

Rendiconti Lincei - Matematica E Applicationi 19, 3 (2008) 237--245

Mathematics

Dynamical Systems

Scientific paper

Nonnegative measure-valued solutions of the continuity equation are uniquely determined by their initial condition, if the characteristic ODE associated to the velocity field has a unique solution. In this paper we give a partial extension of this result to signed measure-valued solutions, under a quantitative two-sided Osgood condition on the velocity field. Our results extend those obtained for log-Lipschitz vector fields by Bahouri and Chemin.

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