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 \(1\le p\le \infty \), and if \(p\ge 3/2\), 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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This research has been supported by the ERC Starting Grant 676675 FLIRT. Gennaro Ciampa and Stefano Spirito acknowledge the support of INdAM-GNAMPA.
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Communicated by Dr. Peter Constantin.
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Ciampa, G., Crippa, G. & Spirito, S. Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy. J Nonlinear Sci 30, 2787–2820 (2020). https://doi.org/10.1007/s00332-020-09635-8
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DOI: https://doi.org/10.1007/s00332-020-09635-8