Journal ArticleDOI
Bifurcation of a periodic solution of the Navier-Stokes equations into an invariant torus
Citations
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Journal ArticleDOI
Time-Periodic Solutions to the Full Navier–Stokes–Fourier System
TL;DR: In this paper, the authors considered the Navier-Stokes-Fourier system with a time-periodic external force and showed the existence of at least one weak time periodic solution to the problem under the basic hypothesis that the system is allowed to dissipate the thermal energy through the boundary.
Journal ArticleDOI
Bifurcation and stability of nT-periodic solutions branching from T-periodic solutions at points of resonance
Gérard Iooss,Daniel D. Joseph +1 more
Book ChapterDOI
Mathematical Theory of Bifurcation
TL;DR: In this paper, the authors considered the boundary value problem of column bifurcation and showed that as λ exceeds π2, a new family of solutions appear and the column buckles.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
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
On the Navier-Stokes initial value problem. I
TL;DR: In this article, the authors considered the Navier-Stokes equation for 3-dimensional flows and deduced the existence theorems for 3D flows through a Hilbert space approach, making use of the theory of fractional powers of operators.
Book
Topics in stability and bifurcation theory
TL;DR: In this paper, the mathematical problems of hydrodynamic stability and topological degree theory and applications are discussed. But the real world is not considered. And there is no solution to the nonlinear elliptic boundary value problems of second order.