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 R2 / Bonicatto, Paolo; Marconi, Elio. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - 46:12(2021), pp. 2235-2267. [10.1080/03605302.2021.1931883]
Regularity estimates for the flow of BV autonomous divergence-free vector fields in R2
Bonicatto, Paolo;
2021-01-01
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 | Dimensione | Formato | |
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BM_Regularity estimates for the flow of BV autonomous divergence free vector fields in R2.pdf
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