On the Extension of Onsager's Conjecture for General Conservation Laws

Abstract

The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "universality" of the Onsager exponent, $\alpha >1/3$, concerning the regularity of the solutions, say in $C^{0,\alpha }$, that guarantees the conservation of the generalized entropy; regardless of the structure of the genuine nonlinearity in the underlying system.

References in corpus (5)

• Regularity and Energy Conservation for the Compressible Euler Equations
• Onsager's Conjecture for the Incompressible Euler Equations in Bounded Domains
• Mathematics and Turbulence: where do we stand?
• Energy conservation for the weak solutions of the compressible Navier-Stokes equations
• A note on weak solutions of conservation laws and energy/entropy conservation

Cited by in corpus (6)

• 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
• On Energy Conservation for the Hydrostatic Euler Equations: An Onsager Conjecture
• Onsager's Conjecture for Subgrid Scale $\alpha$-Models of Turbulence
• The role of density in the energy conservation for the isentropic compressible Euler equations
• An endpoint case of the renormalization property for therelativistic Vlasov-Maxwell system