Onsager and the theory of hydrodynamic turbulence

By Gregory L. Eyink, Katepalli R. Sreenivasan. 2006

452 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4699b57ec37377543c8c91ff65bdab86ad965055

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In Biomedical Engineering

In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

On Nonperiodic Euler Flows with Hölder Regularity (2014, background): “There Onsager stated that energy is conserved by periodic solutions in the class L∞t C x if α > 1/3, and conjectured that energy conservation may fail for such solutions if α < 1/3 (see [15,17] for detailed expositions).”
Anomalous dissipation for 1/5-Hölder Euler flows (2015, unknown): “We refer the interested reader to [15, 22, 14].”
Statistical mechanics of two-dimensional and geophysical flows (2011, background): “The RSM theory includes the previous Onsager, Kraichnan, Salmon– Holloway–Hendershott and Bretherton-Haidvogel theories and determines the particular limits 1 within which those give relevant predictions and general results.”
Convex integration and phenomenologies in turbulence (2019, methodology): “For a detailed study of turbulence theories we refer the reader to the books [6, 149, 150, 81, 79, 194], the surveys papers with a mathematical perspective [32, 66, 165, 33, 71, 180, 5, 69], and to the references therein.”
On the Euler equations of incompressible fluids (2007, background): “Turbulence theory and practice is rather solidly anchored in this fact ([80], [84], [117]).”
Lectures on the Onsager conjecture (2010, methodology): “Let us suppose that we have an ensemble average h�i which measures statistical quantities of the system ( 5). In his unpublished notes (see Eyink and Sreenivasan [ 25 ] for a detailed historical account) Onsager reproduces a formula similar to what is known as K´ arm´ an-Howarth-Monin relation: ∂th ”
Dissipative Euler Flows with Onsager‐Critical Spatial Regularity (2014, background): “The relation between nonuniqueness and nonconservation of the energy for various classes of weak solutions is not yet clear.”
Lecture notes on Generalised Hydrodynamics (2019, unknown): “See for instance [130] and [131]6.”
Beyond Kolmogorov cascades (2019, background): “His finding remained unnoticed for a long time (Eyink & Sreenivasan 2006).”
h-Principles for the Incompressible Euler Equations (2012, background): “part of the conjecture was proved in [14] and [4] (see also [13]).”
Dissipative Euler Flows and Onsager's Conjecture (2012, background): “also [18]) that this should be the case.”