Citations
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Journal ArticleDOI
Geometric statistics in turbulence
TL;DR: The author presents results concerning scaling exponents in turbulence and estimates the average dissipation rate, the average dimension of level sets, and a class of two-dimensional equations that are useful models of incompressible dynamics.
Journal ArticleDOI
On the Euler equations of incompressible fluids
TL;DR: Some of the open problems related to the incompressible Euler equations, with emphasis on the blowup problem, the inviscid limit and anomalous dissipation, are described in this paper.
Journal ArticleDOI
Energy dissipation in body-forced turbulence
Charles R. Doering,Ciprian Foias +1 more
TL;DR: In this article, the authors derived bounds on the bulk rate of energy dissipation in body-force-driven steady-state turbulence from the incompressible Navier-Stokes equations, where the prefactors depend only on the functional shape of the body force and not on its magnitude or any other length scales in the force, the domain or the flow.
Book ChapterDOI
Euler Equations, Navier-Stokes Equations and Turbulence
TL;DR: The Navier-Stokes equations as mentioned in this paper are a viscous regularization of the Euler equations, which are still an enigma, and the Reynolds equations are still a riddle.
References
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Journal ArticleDOI
Linear Operators. Part I: General Theory.
TL;DR: Dunford and Schwartz as discussed by the authors provided a comprehensive survey of the general theory of linear operations, together with applications to the diverse fields of more classical analysis, and emphasized the significance of the relationships between the abstract theory and its applications.
Journal ArticleDOI
Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969;
Journal Article
Statistical study of Navier-Stokes equations, I
Journal Article
Teoremi di tipo locale per il sistema di Navier-Stokes e stabilità delle soluzioni stazionarie
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.unipd.org/legal. php) of the agreement with the Rendiconti del Seminario Matematico della Università di Padova are discussed.
Journal ArticleDOI
Sur les solutions statistiques des équations de Navier-Stokes
Ciprian Foias,G. Prodi +1 more
TL;DR: In this paper, a preuve nouvelle de notre theoreme d'existence des solutions statistiques des equations de Navier-Stokes (voir[6], § 3) is revealed.