Dissipative Euler flows with Onsager-critical spatial regularity

We will briefly outline the story of the step-by-step proof of Onsager's conjecture by Convex Integration and then present one single step: a result by T. Buckmaster, C. de Lellis and L. Székelyhidi (CPAM, 2016). In this paper, the critical spatial 1/3-Hölder regularity was achieved, but only in an "integrable in time" sense and not, as conjectured, uniformly in time. This requires an elaborate inhomogeneous treatment of the time interval, which we will review in detail.