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 Lp with 1 ≤ p≤ ∞, and 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.
Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy
Ciampa G.;
2020
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 Lp with 1 ≤ p≤ ∞, and 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.
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