Linear transport equations with non Lipschitz continuous drift may have non uniqueness of weak solutions. We introduce a suitable random perturbation in this equation. When the drift is Holder continuous and satisfies other integrability properties we first prove the existence of a flow of diffeomorphisms for the equation of characteristics and then prove uniqueness of weak solutions.
Well-posedness of the transport equation by stochastic perturbation
Flandoli, F.;
2010
Abstract
Linear transport equations with non Lipschitz continuous drift may have non uniqueness of weak solutions. We introduce a suitable random perturbation in this equation. When the drift is Holder continuous and satisfies other integrability properties we first prove the existence of a flow of diffeomorphisms for the equation of characteristics and then prove uniqueness of weak solutions.File in questo prodotto:
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