Skip to Main content Skip to Navigation
New interface
Journal articles

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

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [26 references]  Display  Hide  Download
Contributor : François Bouchut Connect in order to contact the contributor
Submitted on : Tuesday, August 18, 2015 - 5:06:26 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM
Long-term archiving on: : Thursday, November 19, 2015 - 10:57:51 AM


Files produced by the author(s)



Anna Bohun, François Bouchut, Gianluca Crippa. Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy. Nonlinear Analysis: Theory, Methods and Applications, 2016, 132, pp.160-172. ⟨10.1016/⟩. ⟨hal-01184975⟩



Record views


Files downloads