Journal ArticleDOI
Existence and nonuniqueness of rectangular solutions of the Bénard problem
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1968-01-01. It has received 150 citations till now.read more
Citations
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Journal ArticleDOI
Numerical solution of the Navier-Stokes equations
TL;DR: In this paper, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Journal ArticleDOI
On the nature of turbulence
David Ruelle,Floris Takens +1 more
TL;DR: A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed in this article, where the authors propose a mechanism for generating turbulence in a dissipative system with respect to dissipative energy.
Journal ArticleDOI
Bifurcation from simple eigenvalues
TL;DR: In this article, a general version of the main problem of bifurcation theory, given p ϵ C, determine the structure of G−1{0} in some neighborhood of p.
Book ChapterDOI
Numerical Solution of the Navier-Stokes Equations*
TL;DR: In this article, a finite-difference method for solving the time-dependent Navier-Stokes equations for an incompressible fluid is introduced, which is equally applicable to problems in two and three space dimensions.
Book ChapterDOI
On the Nature of Turbulence
David Ruelle,Floris Takens +1 more
TL;DR: A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed in this paper, where the authors propose a mechanism for generating turbulence in a dissipative system with respect to dissipative energy.
References
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Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Methods of Mathematical Physics
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
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.