We consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we show that the Lipschitz constant grows at most linearly in time. As a consequence we deduce that both geometric and analytical mixing have a lower bound of order (Formula presented.) as (Formula presented.).

Regularity estimates for the flow of BV autonomous divergence-free vector fields in R^2

Marconi E.
2021

Abstract

We consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we show that the Lipschitz constant grows at most linearly in time. As a consequence we deduce that both geometric and analytical mixing have a lower bound of order (Formula presented.) as (Formula presented.).
File in questo prodotto:
File Dimensione Formato  
BM-Regularity-CPDE.pdf

Accesso riservato

Tipologia: Published (Publisher's Version of Record)
Licenza: Accesso privato - non pubblico
Dimensione 742.12 kB
Formato Adobe PDF
742.12 kB Adobe PDF Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3456023
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 6
  • OpenAlex ND
social impact