Velocity-vorticity geometric constraints for the energy conservation of 3D ideal incompressible fluids

2024/05/14 by Berselli, Luigi C., Sannipoli, Rossano
#Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35Q31 #Secondary 76B03

paper · doi:10.48550/arxiv.2405.08461

Abstract

In this paper we consider the 3D Euler equations and we first prove a criterion for energy conservation for weak solutions with velocity satisfying additional assumptions in fractional Sobolev spaces with respect to the space variables, balanced by proper integrability with respect to time. Next, we apply the criterion to study the energy conservation of solution of the Beltrami type, carefully applying properties of products in (fractional and possibly negative) Sobolev spaces and employing a suitable bootstrap argument.

Related

• Energy conservation for 3D Euler and Navier-Stokes equations in a bounded domain. Applications to Beltrami flows
• Three results on the Energy conservation for the 3D Euler equations
• Energy conservation of weak solutions for the incompressible Euler equations via vorticity
• On the energy of inviscid singular flows
• Energy conservation and Onsager's conjecture for the Euler equations