Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

Non-uniqueness and prescribed energy for the continuity equation

Pages: 1937 – 1947

(Fast Communication)



Gianluca Crippa (Departement Mathematik und Informatik, Universität Basel, Switzerland)

Nikolay Gusev (Moscow, Russia)

Stefano Spirito (Gran Sasso Science Institute (GSSI), L’Aquila, Italy)

Emil Wiedemann (Hausdorff Center for Mathematics and Mathematical Institute, Universität Bonn, Germany)


In this note, we provide new non-uniqueness examples for the continuity equation by constructing infinitely many weak solutions with prescribed energy.


transport and continuity equations, non-uniqueness, non-conservation of energy, renormalization, convex integration

2010 Mathematics Subject Classification

35A02, 35F10

Published 19 August 2015