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Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy
JournalArticle (Originalarbeit in einer wissenschaftlichen Zeitschrift)
 
ID 3343823
Author(s) Bohun, Anna; Bouchut, François; Crippa, Gianluca
Author(s) at UniBasel Crippa, Gianluca
Year 2016
Title Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy
Journal Nonlinear Analysis: Theory, Methods & Applications
Volume 132
Pages / Article-Number 160-172
Abstract We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated to vector fields with gradient given by a singular integral in order to define Lagrangian solutions, for which the vorticity is transported by the flow. We prove strong stability of these solutions via strong convergence of the flow, under the only assumption of L1 weak convergence of the initial vorticity. The existence of Lagrangian solutions to the Euler system follows for arbitrary L1 vorticity. Relations with previously known notions of solutions are established.
Publisher Elsevier
ISSN/ISBN 0362-546X
edoc-URL http://edoc.unibas.ch/40184/
Full Text on edoc Restricted
Digital Object Identifier DOI 10.1016/j.na.2015.11.004
ISI-Number WOS:000366665000009
Document type (ISI) Article
 
   

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