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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… Click to show full abstract
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:
vector;
flow autonomous;
differentiability properties;
autonomous vector;
vector fields;
properties flow
Journal Title: Journal of Differential Equations
Year Published: 2021
Link to full text (if available)
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Journal Title: Journal of Differential Equations
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!