A uniqueness result for the continuity equation in two dimensions
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
ID 2189534
Author(s) Alberti, Giovanni; Bianchini, Stefano; Crippa, Gianluca
Author(s) at UniBasel Crippa, Gianluca
Year 2014
Title A uniqueness result for the continuity equation in two dimensions
Journal Journal of the European Mathematical Society
Volume 16
Number 2
Pages / Article-Number 201-234
Keywords Continuity equation, transport equation, uniqueness of weak solutions, weak Sard property, disintegration of measures, coarea formula
Abstract We characterize the autonomous, divergence-free vector fields b on the plane such that the Cauchy problem for the continuity equation partial derivative(t)u + div(bu) = 0 admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential f associated to b. As a corollary we obtain uniqueness under the assumption that the curl of b is a measure. This result can be extended to certain nonautonomous vector fields b with bounded divergence.
Publisher EMS
ISSN/ISBN 1435-9855
edoc-URL http://edoc.unibas.ch/dok/A6183952
Full Text on edoc Available
Digital Object Identifier DOI 10.4171/JEMS/431
ISI-Number WOS:000331327500001
Document type (ISI) Article

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