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, FRANCO;
2010-01-01
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:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
