The full text of this article is unavailable through your IP address: 3.147.73.117
Contents Online
Communications in Mathematical Sciences
Volume 20 (2022)
Number 3
Energy conservation for 2D Euler with vorticity in $L (\operatorname{log} L)^\alpha$
Pages: 855 – 875
DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n3.a10
Author
Abstract
In these notes we discuss the conservation of the energy for weak solutions of the two-dimensional incompressible Euler equations. Weak solutions with vorticity in $L^{\infty}_t L^p_x$ with $p \geq 3/2$ are always conservative, while for less integrable vorticity the conservation of the energy may depend on the approximation method used to construct the solution. Here we prove that the canonical approximations introduced by DiPerna and Majda provide conservative solutions when the initial vorticity is in the class $L (\operatorname{log} L)^\alpha$ with $\alpha \gt 1/2$.
Keywords
2D Euler equations, vanishing viscosity, vortex methods, conservation of energy
2010 Mathematics Subject Classification
35Q31, 35Q35
Received 3 March 2021
Received revised 28 September 2021
Accepted 6 October 2021
Published 21 March 2022