2 papers
math.AP2021
Non-uniqueness of integral curves for autonomous Hamiltonian vector fields
Vikram Giri, Massimo Sorella
In this work we prove the existence of an autonomous Hamiltonian vector field in W^{1,r}(T^d;R^d) with r< d-1and d>=4 for which the associated transport equation has non-unique pos…
math.AP2020
Smoothing does not give a selection principle for transport equations with bounded autonomous fields
Camillo De Lellis, Vikram Giri
We give an example of a bounded divergence free autonomous vector field in (and of a nonautonomous bounded divergence free vector field in ) and of a bou…