On the control of the chaotic attractors of the 2-d Navier-Stokes equations

DOI10.1063/1.4978682zbMath1390.37063OpenAlexW2600674529WikidataQ47907235 ScholiaQ47907235MaRDI QIDQ4642572

Nejib Smaoui, Mohamed Zribi

Publication date: 23 May 2018

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4978682

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Navier-Stokes equations (35Q30) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (1)

Symmetries, dynamics, and control for the 2D Kolmogorov flow

Uses Software

• DSTool

Cites Work

• Unnamed Item
• Unnamed Item
• Adaptive control of a seven mode truncation of the Kolmogorov flow with drag
• On approximate inertial manifolds to the Navier-Stokes equations
• On some control problems in fluid mechanics
• Fault tolerant control using sliding modes with on-line control allocation
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A five-mode truncation of the Navier-Stokes equations on a three- dimensional torus
• Inertial manifolds for nonlinear evolutionary equations
• On the dimension of the attractors in two-dimensional turbulence
• A five-dimensional truncation of the plane incompressible Navier-Stokes equations
• Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
• Bifurcations of a steady-state solution to the two-dimensional Navier-Stokes equations
• Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds
• Upper bound on the dimension of the attractor for nonhomogeneous Navier-Stokes equations
• Nonlinear control of incompressible fluid flow: Application to Burgers' equation and 2D channel flow
• Symmetries and dynamics for 2-D Navier-Stokes flow
• Modified post-bifurcation dynamics and routes to chaos from double-Hopf bifurcations in a hyperchaotic system
• Common periodic behavior in larger and larger truncations of the Navier-Stokes equations.
• Double Hopf bifurcations and chaos of a nonlinear vibration system
• Dynamics and control of the seven-mode truncation system of the 2-d Navier-Stokes equations
• Transition to chaos in a fluid motion system
• On the nature of turbulence
• Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations
• Attractors of partial differential evolution equations and estimates of their dimension
• Timely Communication:Symmetry and the Karhunen--Loève Analysis
• Finite-dimensional approximation and control of non-linear parabolic PDE systems
• Self-similarity in incompressible Navier-Stokes equations
• Deterministic Nonperiodic Flow
• Chaotic behavior of a Galerkin model of a two-dimensional flow

This page was built for publication: On the control of the chaotic attractors of the 2-d Navier-Stokes equations