Calculus of Variations and Geometric Measure Theory

E. Marconi

Differentiability properties of the flow of 2d autonomous vector fields

created by marconi on 19 Jan 2021
modified on 24 Aug 2021


Accepted Paper

Inserted: 19 jan 2021
Last Updated: 24 aug 2021

Journal: Journal of Differential Equations
Year: 2021


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.