Energy equality for the Navier-Stokes equations in weak-in-time Onsager spaces

Abstract

Onsager's conjecture for the 3D Navier-Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note we establish energy equality for weak solutions in a large class of function spaces. These conditions are weak-in-time with optimal space regularity and therefore weaker than all previous classical results. Heuristics using intermittency argument suggests the possible sharpness of our results.

References in corpus (1)

• On admissibility criteria for weak solutions of the Euler equations

Cited by in corpus (1)

• Anomalous dissipation, anomalous work, and energy balance for smooth solutions of the Navier-Stokes equations