edoc

Lagrangian flows for vector fields with anisotropic regularity

Bohun, Anna and Bouchut, François and Crippa, Gianluca. (2016) Lagrangian flows for vector fields with anisotropic regularity. Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, 33 (6). pp. 1409-1429.

[img]
Preview
PDF - Accepted Version
Available under License CC BY-NC-ND (Attribution-NonCommercial-NoDerivatives).

891Kb

Official URL: http://edoc.unibas.ch/40176/

Downloads: Statistics Overview

Abstract

We prove quantitative estimates for flows of vector fields subject to anisotropic regularity conditions: some derivatives of some components are (singular integrals of) measures, while the remaining derivatives are (singular integrals of) integrable functions. This is motivated by the regularity of the vector field in the Vlasov-Poisson equation with measure density. The proof exploits an anisotropic variant of the argument in [Crippa-De Lellis, Bouchut-Crippa] and suitable estimates for the difference quotients in such anisotropic context. In contrast to regularization methods, this approach gives quantitative estimates in terms of the given regularity bounds. From such estimates it is possible to recover the well posedness for the ordinary differential equation and for Lagrangian solutions to the continuity and transport equations.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Elsevier
ISSN:0294-1449
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:17 Nov 2016 08:08
Deposited On:17 Nov 2016 08:08

Repository Staff Only: item control page