Differentiability properties of the flow of 2d autonomous vector fields

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.

References in corpus (2)

• Sharp regularity estimates for solutions of the continuity equation drifted by Sobolev vector fields
• Regularity estimates for the flow of BV autonomous divergence free vector fields in ${\mathbb{R}}^2$

Cited by in corpus (1)

• Initial-boundary value problems for merely bounded nearly incompressible vector fields in one space dimension