Lagrangian flows for vector fields with gradient given by a singular integral
Analysis of PDEs
2013-06-28 v1 Functional Analysis
Abstract
We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an function. Such estimates allow to prove existence, uniqueness, quantitative stability and compactness for the flow, going beyond the theory. We illustrate the related well-posedness theory of Lagrangian solutions to the continuity and transport equations.
Cite
@article{arxiv.1208.6374,
title = {Lagrangian flows for vector fields with gradient given by a singular integral},
author = {François Bouchut and Gianluca Crippa},
journal= {arXiv preprint arXiv:1208.6374},
year = {2013}
}