Global stability analysis of fluid flows using sum-of-squares

DOI10.1016/j.physd.2011.12.008zbMath1331.76050arXiv1101.1043OpenAlexW1516285919MaRDI QIDQ429219

Paul J. Goulart, Sergei Chernyshenko

Publication date: 26 June 2012

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1043

zbMATH Keywords

Lyapunov methodsNavier-Stokessum-of-squaresflow stability

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Navier-Stokes equations (35Q30) Hydrodynamic stability (76E99)

Related Items (17)

Analysis of Linear Partial Differential Equations Using Convex Optimization ⋮ On long-term boundedness of Galerkin models ⋮ Flow regimes in a simplified Taylor-Couette-type flow model ⋮ Polynomial sum of squares in fluid dynamics: a review with a look ahead ⋮ Sum-of-squares approach to feedback control of laminar wake flows ⋮ Verification Methods for the Lyapunov–Krasovskii Functional Inequalities ⋮ Global stability analysis of fluid flows using sum-of-squares ⋮ Exact energy stability of Bénard–Marangoni convection at infinite Prandtl number ⋮ Bounding extrema over global attractors using polynomial optimisation ⋮ Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming ⋮ Finding Extremal Periodic Orbits with Polynomial Optimization, with Application to a Nine-Mode Model of Shear Flow ⋮ Bounds for Rayleigh–Bénard convection between free-slip boundaries with an imposed heat flux ⋮ A framework for input–output analysis of wall-bounded shear flows ⋮ Bounding Extreme Events in Nonlinear Dynamics Using Convex Optimization ⋮ Efficient semidefinite programming with approximate ADMM ⋮ Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization ⋮ Geometrical dependence of optimal bounds in Taylor–Couette flow

Uses Software

• SeDuMi
• YALMIP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global stability analysis of fluid flows using sum-of-squares
• On the stability of viscous fluid motions
• Semidefinite programming relaxations for semialgebraic problems
• The Energy Operator and New Scaling Relations for the Incompressible Navier--Stokes Equations
• Semidefinite optimization
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition
• Applied Analysis of the Navier-Stokes Equations
• Pre- and Post-Processing Sum-of-Squares Programs in Practice
• Periodic Orbits and Chaotic Sets in a Low-Dimensional Model for Shear Flows
• Handbook of semidefinite programming. Theory, algorithms, and applications

This page was built for publication: Global stability analysis of fluid flows using sum-of-squares