Onsager's 'ideal turbulence'theory

G Eyink - Journal of Fluid Mechanics, 2024‏ - cambridge.org
In 1945–1949, Lars Onsager made an exact analysis of the high-Reynolds-number limit for
individual turbulent flow realisations modelled by incompressible Navier–Stokes equations …

Dissipation in Onsager's Critical Classes and Energy Conservation in with and Without Boundary

L De Rosa, M Inversi - Communications in Mathematical Physics, 2024‏ - Springer
This paper is concerned with the incompressible Euler equations. In Onsager's critical
classes we provide explicit formulas for the Duchon–Robert measure in terms of the …

Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit

TD Drivas, HQ Nguyen - Journal of Nonlinear Science, 2019‏ - Springer
We prove that if the local second-order structure function exponents in the inertial range
remain positive uniformly in viscosity, then any spacetime L^ 2 L 2 weak limit of Leray–Hopf …

An Onsager singularity theorem for Leray solutions of incompressible Navier–Stokes

TD Drivas, GL Eyink - Nonlinearity, 2019‏ - iopscience.iop.org
We study in the inviscid limit the global energy dissipation of Leray solutions of
incompressible Navier–Stokes on the torus, assuming that the solutions have norms for …

Josephson-Anderson relation and the classical D'Alembert paradox

GL Eyink - Physical Review X, 2021‏ - APS
Generalizing the prior work of PW Anderson and ER Huggins, we show that a “detailed
Josephson-Anderson relation” holds for drag on a finite body held at rest in a classical …

On the endpoint regularity in Onsager's conjecture

P Isett - Analysis & PDE, 2024‏ - msp.org
Onsager's conjecture states that the conservation of energy may fail for three-dimensional
incompressible Euler flows with Hölder regularity below 1 3. This conjecture was recently …

[HTML][HTML] Energy conservation for weak solutions of incompressible fluid equations: The Hölder case and connections with Onsager's conjecture

LC Berselli - Journal of Differential Equations, 2023‏ - Elsevier
In this paper we give elementary proofs of energy conservation for weak solutions to the
Euler and Navier-Stokes equations in the class of Hölder continuous functions, relaxing …

Energy equalities for compressible Navier–Stokes equations

QH Nguyen, PT Nguyen, BQ Tang - Nonlinearity, 2019‏ - iopscience.iop.org
The energy equalities of compressible Navier–Stokes equations with general pressure law
and degenerate viscosities are studied. By using a unified approach, we give sufficient …

On the support of anomalous dissipation measures

L De Rosa, TD Drivas, M Inversi - Journal of Mathematical Fluid …, 2024‏ - Springer
By means of a unifying measure-theoretic approach, we establish lower bounds on the
Hausdorff dimension of the space-time set which can support anomalous dissipation for …

Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws

C Bardos, P Gwiazda… - … of the Royal …, 2019‏ - royalsocietypublishing.org
We show that weak solutions of general conservation laws in bounded domains conserve
their generalized entropy, and other respective companion laws, if they possess a certain …