Communications in Mathematical Sciences

Volume 13 (2015)

Number 7

Non-uniqueness and prescribed energy for the continuity equation

Pages: 1937 – 1947

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2015.v13.n7.a12

Authors

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)

Abstract

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

Keywords

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

2010 Mathematics Subject Classification

35A02, 35F10

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