Stability of plane Couette flows with respect to small periodic perturbations

DOI10.1016/j.na.2009.02.034zbMath1173.35627OpenAlexW2063428703MaRDI QIDQ1029411

Horst Heck, Hideo Kozono, Hyun-Seok Kim

Publication date: 10 July 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.02.034

zbMATH Keywords

stabilityNavier-Stokes equationsplane Couette flow

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Parallel shear flows in hydrodynamic stability (76E05)

Related Items (7)

Stability of a two-dimensional Poiseuille-type flow for a viscoelastic fluid ⋮ The resolvent technique for investigating the stability of plane Couette flow: bounds for the pressure terms ⋮ Stability of a two‐dimensional stationary rotating flow in an exterior cylinder ⋮ Rigorous justification of the hydrostatic approximation for the primitive equations by scaled Navier–Stokes equations* ⋮ On the asymptotic stability of a stratified flow of the 2D non-resistive incompressible MHD equations ⋮ On the Exponential Stability of a Stratified Flow to the 2D Ideal MHD Equations with Damping ⋮ The hydrostatic approximation for the primitive equations by the scaled Navier-Stokes equations under the no-slip boundary condition

Cites Work

• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Resolvent estimates for the Stokes operator on an infinite layer.
• On a larger class of stable solutions to the Navier-Stokes equations in exterior domains
• On a resolvent estimate of the Stokes equation on an infinite layer.
• On a resolvent estimate of the Stokes equation on an infinite layer. II: \( \lambda=0\) case
• Weighted \(L^q\)-Helmholtz decompositions in infinite cylinders and in infinite layers.
• Perturbation theory for linear operators.
• Stability of plane-parallel Couette flow
• On a rigorous resolvent estimate for plane Couette flow
• On vector-valued Fourier multiplier theorems
• One-Parameter Semigroups for Linear Evolution Equations
• Resolvent Estimates for Plane Couette Flow
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