Inviscid K41-Onsager conjecture for globally dissipative Euler flows

Let $I$ be an open interval, and let $(v,p)$ be a weak solution of the incompressible Euler equations on $I \times \mathbb{T}^3$. Assume that $v \in L_t^\infty C_x^{1/3}$ and that it satisfies the local energy inequality, with its left-hand side not identically zero. Inviscid K41-Onsager conjecture. There exists such an interval $I$ and such a weak solution $(v,p)$. This is the analogue for globally dissipative incompressible Euler flows of the Onsager conjecture on anomalous energy dissipation. The source presents the existence assertion, together with the associated uniqueness question, as a primary focus; no resolution of this conjecture is supplied here.