Journal ArticleDOI
Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer
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In this article, it was shown that a solution of incompressible Euler equations with Holder continuous velocity of order h > 1 3 conserves kinetic energy, but not necessarily if h ≤ 1 3.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1994-11-15. It has received 385 citations till now. The article focuses on the topics: Dissipation & Turbulence kinetic energy.read more
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Onsager's conjecture on the energy conservation for solutions of Euler's equation
TL;DR: In this article, a simple proof of a result conjectured by Onsager on energy conservation for weak solutions of Euler's equation is given for weak Euler solvers.
Journal ArticleDOI
Onsager and the theory of hydrodynamic turbulence
TL;DR: Onsager's contributions to the field of hydrodynamic turbulence are summarized in this paper, with a discussion of the historical context of the work and a brief speculation as to why Onsager may have chosen not to publish several significant results.
Journal ArticleDOI
The Euler equations as a differential inclusion
TL;DR: In this article, a new point of view on weak solutions of the Euler equations is proposed, describing the motion of an ideal incompressible fluid in R n with n 2.
Journal ArticleDOI
Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
Jean Duchon,Raoul Robert +1 more
TL;DR: In this article, the authors studied the local equation of energy for weak solutions of weak Navier-Stokes and Euler equations and gave a simple proof of Onsager's conjecture on energy conservation for the three-dimensional Euler equation.
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The Euler equations as a differential inclusion
TL;DR: In this paper, a new point of view on weak solutions of the Euler equations is proposed, which describes the motion of an ideal incompressible fluid in the plane with constant velocity and pressure, and gives transparent proofs of several celebrated results of V. Scheffer and A. Shnirelman.
References
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Book
Ten lectures on wavelets
TL;DR: This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.
Journal ArticleDOI
Ten Lectures on Wavelets
TL;DR: In this article, the regularity of compactly supported wavelets and symmetry of wavelet bases are discussed. But the authors focus on the orthonormal bases of wavelets, rather than the continuous wavelet transform.
Journal Article
The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds' Numbers
TL;DR: In this article, the authors consider the problem of finding the components of the velocity at every point of a point with rectangular cartesian coordinates x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8.
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A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number
TL;DR: Kolmogorov and Oboukhov as discussed by the authors investigated the local structure of turbulence at high Reynolds number, based on Richardson's idea of the existence in the turbulent flow of vortices on all possible scales.
Book
An Introduction to Harmonic Analysis
TL;DR: In this article, the convergence of Fourier series on T and convergence of the conjugate function on T was studied, where T is the length of the line of a vector.