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Onsager's 'ideal turbulence'theory
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 …
individual turbulent flow realisations modelled by incompressible Navier–Stokes equations …
Dissipation in Onsager's Critical Classes and Energy Conservation in with and Without Boundary
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 …
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
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 …
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
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 …
incompressible Navier–Stokes on the torus, assuming that the solutions have norms for …
Josephson-Anderson relation and the classical D'Alembert paradox
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 …
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 …
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
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 …
Euler and Navier-Stokes equations in the class of Hölder continuous functions, relaxing …
Energy equalities for compressible Navier–Stokes equations
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 …
and degenerate viscosities are studied. By using a unified approach, we give sufficient …
On the support of anomalous dissipation measures
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 …
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
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 …
their generalized entropy, and other respective companion laws, if they possess a certain …