Contents Online
Communications in Mathematical Sciences
Volume 13 (2015)
Number 7
Non-uniqueness and prescribed energy for the continuity equation
Pages: 1937 – 1947
(Fast Communication)
DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n7.a12
Authors
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
Published 19 August 2015