Instability for the Navier-Stokes equations on the 2-dimensional torus and a lower bound for the Hausdorff dimension of their global attractors

DOI10.1007/BF02096584zbMath0778.76021MaRDI QIDQ1200486

Vincent Xiaosong Liu

Publication date: 16 January 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Fourier expansionperiodic boundary conditionscontinued fractionsnegative eigenvaluesexternal forcerecurrent relationsunstable stationary solution

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Navier-Stokes equations (35Q30)

Related Items

Symmetries, dynamics, and control for the 2D Kolmogorov flow ⋮ Remarks on the navier-stokes equations on the two and three dimensional torus ⋮ Instability of unidirectional flows for the 2D Navier-Stokes equations and related \(\alpha\)-models ⋮ Time dependent periodic Navier-Stokes flows on a two-dimensional torus ⋮ Symmetries and dynamics for 2-D Navier-Stokes flow ⋮ Nonlinear instability for the Boussinesq equations with diabatic forcing ⋮ Stabilization of 2D Navier-Stokes equations by means of actuators with locally supported vorticity ⋮ Dynamics and control of the seven-mode truncation system of the 2-d Navier-Stokes equations ⋮ Long-time behavior of Navier-Stokes flow on a two-dimensional torus excited by an external sinusoidal force ⋮ A sharp lower bound for the Hausdorff dimension of the global attractors of the 2D Navier-Stokes equations

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