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Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy

Bohun, Anna and Bouchut, François and Crippa, Gianluca. (2016) Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy. Nonlinear Analysis: Theory, Methods & Applications, 132. pp. 160-172.

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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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Elsevier
ISSN:0362-546X
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:11 Oct 2017 12:06
Deposited On:05 Apr 2016 13:20

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