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On the failure of the chain rule for the divergence of Sobolev vector fields
Miriam Buck, Stefano Modena
We construct a large class of incompressible vector fields with Sobolev regularity, in dimension , for which the chain rule problem has a negative answer. In particular,…
On some recent results concerning non-uniqueness for the transport equation
Stefano Modena
In these notes we present some recent results concerning the non-uniqueness of solutions to the transport equation, obtained in collaboration with Gabriel Sattig and Laszlo Szekely…
Convex integration solutions to the transport equation with full dimensional concentration
Stefano Modena, Gabriel Sattig
We construct infinitely many incompressible Sobolev vector fields on the periodic domain for which uniqueness of solutions to the transp…
Non-renormalized solutions to the continuity equation
Stefano Modena, László Székelyhidi
We show that there are continuous, (), incompressible vector fields for which uniqueness of solutions to the continuity equation fails.