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arXiv · 2101.07871

Differentiability properties of the flow of 2d autonomous vector fields

Elio Marconi
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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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Elio Marconi. 2021-01-19. Differentiability properties of the flow of 2d autonomous vector fields. https://doi.org/10.1016/j.jde.2021.08.025

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