Padua Research Archive, l’archivio istituzionale della produzione scientifica dell’Università degli Studi di Padova, ha lo scopo di raccogliere, documentare, conservare e pubblicare, anche ad accesso aperto, i prodotti della ricerca dell’Ateneo. Padua Research Archive utilizza la piattaforma IRIS (Institutional Research Information System) sviluppata da Cineca.
EnglishWe deal with the uniqueness of distributional solutions to the continuity equation with a Sobolev vector field and with the property of being a Lagrangian solution, that means transported by a flow of the associated ordinary differential equation. We work in a framework of lack of local integrability of the solution, in which the classical DiPerna-Lions theory of uniqueness and Lagrangianity of distributional solutions does not apply due to the insufficient integrability of the commutator. We introduce a general principle to prove that a solution is Lagrangian: we rely on a disintegration along the unique flow and on a new directional Lipschitz extension lemma, used to construct a large class of test functions in the Lagrangian distributional formulation of the continuity equation.
| Titolo: | Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation |
| Autori: | |
| Data di pubblicazione: | 2016 |
| Rivista: | |
| Abstract: | We deal with the uniqueness of distributional solutions to the continuity equation with a Sobolev vector field and with the property of being a Lagrangian solution, that means transported by a flow of the associated ordinary differential equation. We work in a framework of lack of local integrability of the solution, in which the classical DiPerna-Lions theory of uniqueness and Lagrangianity of distributional solutions does not apply due to the insufficient integrability of the commutator. We introduce a general principle to prove that a solution is Lagrangian: we rely on a disintegration along the unique flow and on a new directional Lipschitz extension lemma, used to construct a large class of test functions in the Lagrangian distributional formulation of the continuity equation. |
| Handle: | http://hdl.handle.net/11577/3199463 |
| Appare nelle tipologie: | 01.01 - Articolo in rivista |
File in questo prodotto:
http://hdl.handle.net/11577/3199463
Copyright © 2019