Accepted Paper
Inserted: 19 jan 2021
Last Updated: 24 aug 2021
Journal: Journal of Differential Equations
Year: 2021
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.
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