Statistical solutions and Onsager's conjecture

Abstract

We prove a version of Onsager's conjecture on the conservation of energy for the incompressible Euler equations in the context of statistical solutions, as introduced recently by Fjordholm et al. As a byproduct, we also obtain a new proof for the conservative direction of Onsager's conjecture for weak solutions. Dedicated to Edriss S. Titi on the occasion of his 60th birthday.

References in corpus (2)

• Onsager's Conjecture for the Incompressible Euler Equations in Bounded Domains
• An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

Cited by in corpus (8)

• Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit
• Energy Conservation for the Compressible Euler and Navier-Stokes Equations with Vacuum
• Statistical solutions to the barotropic Navier-Stokes system
• On the conservation of energy in two-dimensional incompressible flows
• The role of density in the energy conservation for the isentropic compressible Euler equations
• Probabilistic Descriptions of Fluid Flow: A Survey
• On entropy conservation for general systems of conservation laws
• $L^2$-Density of Wild Initial Data for the Hypodissipative Navier-Stokes Equations