3 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.AP2021
The four-state problem and convex integration for linear differential operators
Massimo Sorella, Riccardo Tione
We show that the four-state problem for general linear differential operators is flexible. The only flexibility result available in this context is the one for the five-state probl…
math.AP2021
Typicality results for weak solutions of the incompressible Navier--Stokes equations
Maria Colombo, Luigi De Rosa, Massimo Sorella
In this work we show that, in the class of distributional solutions of the incompressible Navier-Stokes system, the ones which are smooth in som…