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arXiv · 1905.09720

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

Gennaro Ciampa·Gianluca Crippa·Stefano Spirito
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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 $1\leq p\leq \infty$. Moreover, if $p\geq 3/2$ 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 $p>1$.

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Gennaro Ciampa, Gianluca Crippa, Stefano Spirito. 2019-05-23. Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy. https://doi.org/10.1007/s00332-020-09635-8

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