A geometric condition implying energy equality for solutions of 3D Navier-Stokes equation

Abstract

We prove that every weak solution $u$ to the 3D Navier-Stokes equation that belongs to the class $L^3{L}^{9/2}$ and $\n u$ belongs to $L^3{L}^{9/5}$ localy away from a 1/2-Hölder continuous curve in time satisfies the generalized energy equality. In particular every such solution is suitable.

10 pages

References in corpus (1)

• Energy conservation and Onsager's conjecture for the Euler equations

Cited by in corpus (3)

• The energy conservation and regularity for the Navier-Stokes equations
• On the energy of inviscid singular flows
• The energy conservation for the Navier-Stokes equations on the Lipschitz domains