Anomalous dissipation for 1/5-Hölder Euler flows

By T. Buckmaster, Camillo De Lellis, Philip Isett, L. Sz'ekelyhidi. 2015

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L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^\infty $$\end{document} Ill-Posedness for a Class of Equations Ari (2019, methodology): “Finally, nonuniqueness of weak solutions was shown by Scheffer [40], Shnirelman [41], De Lellis and Szekelyhidi [17], Isett [26], and Buckmaster [11] for weak solutions of the Euler equations in various “very weak” spaces, the smallest of which is Cαt,x , α 1 5 .”
Onsager's Conjecture for Admissible Weak Solutions (2017, methodology): “The parameter q should be compared to the parameter 1 used in the paper [4].”
Non-uniqueness and h-Principle for Hölder-Continuous Weak Solutions of the Euler Equations (2016, methodology): “The proof is a simplified version of the construction in [3], where we replace Beltrami flows by Mikado flows.”
Nonuniqueness of Weak Solutions to the SQG Equation (2016, methodology): “In [BDLISJ15], highly oscillatory Beltrami waves formed the principle building block in the construction.”
Nonuniqueness of weak solutions to the Navier-Stokes equation (2017, unknown): “In order to better suit our later goal of defining intermittent Beltrami waves, the statements of these propositions are slightly modified from the form they appear in [2], by making the substitution k |k| 7→ ξ.”
Dissipative Euler Flows with Onsager‐Critical Spatial Regularity (2014, methodology): “In the statement above we have introduced the parameters ır;l in order to aid better the comparison with [2].”
Convex integration and phenomenologies in turbulence (2019, methodology): “In earlier papers [48, 49, 16, 14, 103, 17], Beltrami waves were used as the building blocks of the convex”
On Nonperiodic Euler Flows with Hölder Regularity (2014, methodology): “On the periodic torus, the construction of (1/5 − ε)-Hölder solutions that fail to conserve energy was first achieved in [23] improving on initial constructions of (1/10 − ε)-Hölder solutions in [12,14] (see also [1,2] for a shorter proof closer to the scheme of [12,14]).”
Cascades and transitions in turbulent flows (2018, background): “Interestingly enough, recent rigorous progresses meant to prove the Onsager conjecture for the Euler equations have provided a first constructive way to build up weak solutions with a multi-fractal structure [205, 499].”