Regularity estimates for the flow of BV autonomous divergence free vector fields in R^2
| Autor: | Paolo Bonicatto, Elio Marconi |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
37C10
01 natural sciences Divergence symbols.namesake Mathematics - Analysis of PDEs Mixing (mathematics) 34C11 (primary) 35L45 BV vector field Lusin-Lipschitz mixing regular Lagrangian flow FOS: Mathematics Mathematics::Metric Geometry 0101 mathematics Mathematics Applied Mathematics 010102 general mathematics Mathematical analysis 34C11 010101 applied mathematics Flow (mathematics) Bounded function Bounded variation symbols Vector field Analysis Lagrangian Analysis of PDEs (math.AP) |
| Zdroj: | Communications in Partial Differential Equations |
| ISSN: | 0360-5302 |
| DOI: | 10.1080/03605302.2021.1931883 |
| Popis: | 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 $t^{-1}$ as $t \to \infty$. |
| Databáze: | OpenAIRE |
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