# Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy

Ciampa, Gennaro and Crippa, Gianluca and Spirito, Stefano. (2019) Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy. Preprints Fachbereich Mathematik , 2019 (08).

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Official URL: https://edoc.unibas.ch/70739/

## Abstract

We discuss the Lagrangian property and the conservation of the kinetic energy for solutions of the 2D incompressible Euler equations. Existence of Lagrangian solutions is known when the initial vorticity is in $L^p$ with 1≤p≤∞. Moreover, if p≥3/2 all weak solutions are conservative. In this work we prove that solutions obtained via the vortex method are Lagrangian, and that they are conservative if p>1.
Faculties and Departments: 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)12 Special Collections > Preprints Fachbereich Mathematik Ciampa, Gennaro and Crippa, Gianluca Preprint Universität Basel English 30 May 2019 15:23 30 May 2019 15:23

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