Differentiability properties of the flow of 2d autonomous vector fields
Analysis of PDEs
2021-12-20 v1
Abstract
We investigate under which assumptions the flow associated to autonomous planar vector fields inherits the Sobolev or BV regularity of the vector field. We consider nearly incompressible and divergence-free vector fields, taking advantage in both cases of the underlying Hamiltonian structure. Finally we provide an example of an autonomous planar Sobolev divergence-free vector field, such that the corresponding regular Lagrangian flow has no bounded variation.
Keywords
Cite
@article{arxiv.2101.07871,
title = {Differentiability properties of the flow of 2d autonomous vector fields},
author = {Elio Marconi},
journal= {arXiv preprint arXiv:2101.07871},
year = {2021}
}