Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid
From MaRDI portal
Publication:3845020
DOI10.1016/0021-8928(62)90149-1zbMath0108.39501OpenAlexW2083978266MaRDI QIDQ3845020
L. D. Meshalkin, Yakov G. Sinai
Publication date: 1961
Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0021-8928(62)90149-1
Related Items (only showing first 100 items - show all)
A generalized theory of flow forcing by rough topography ⋮ Transitions of zonal flows in a two-layer quasi-geostrophic ocean model ⋮ Nonlinear stability of sinusoidal Euler flows on a flat two-torus ⋮ Singularity formation in the incompressible Euler equation in finite and infinite time ⋮ Chaotic behavior of a Galerkin model of a two-dimensional flow ⋮ A two-dimensional vortex condensate at high Reynolds number ⋮ New Beltrami type solutions to continuum equations for fluidization and their stability ⋮ Secondary fluid flows driven electromagnetically in a two-dimensional extended duct ⋮ Nonlinear dynamics of the viscoelastic Kolmogorov flow ⋮ Bounds on dissipation for Navier-Stokes flow with Kolmogorov forcing ⋮ Spatio-temporal dynamics of forced periodic flows in a confined domain ⋮ Stability of \(\beta\)-plane Kolmogorov flow ⋮ Nonlinear stability of the two-jet Kolmogorov type flow on the unit sphere under a perturbation with nondissipative part ⋮ A computer-assisted proof on the stability of the Kolmogorov flows of incompressible viscous fluid ⋮ Non-ideal instabilities in sinusoidal shear flows with a streamwise magnetic field ⋮ Mechanics of thermohaline interleaving: beyond the empirical flux laws ⋮ Secondary flows from a linear array of vortices perturbed principally by a Fourier mode ⋮ Bifurcation structure of two-dimensional viscous zonal flows on a rotating sphere ⋮ Nonlinear instability in an ideal fluid ⋮ Stratospheric planetary flows from the perspective of the Euler equation on a rotating sphere ⋮ Energy-enstrophy stability of β-plane Kolmogorov flow with drag ⋮ Sharp lower bounds for the dimension of the global attractor of the Sabra shell model of turbulence ⋮ Construction of circle bifurcations of a two-dimensional spatially periodic flow ⋮ New planforms in systems of partial differential equations with Euclidean symmetry ⋮ Variational methods for finding periodic orbits in the incompressible Navier–Stokes equations ⋮ Linear stability and enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere ⋮ Stability of an oscillating Kolmogorov flow ⋮ Rate of the enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere ⋮ Large-scale Kolmogorov flow on the beta-plane and resonant wave interactions ⋮ Modelling the dynamics of nonlinear partial differential equations using neural networks ⋮ 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 ⋮ Instabilities, bifurcations, and nonlinear dynamics in two-dimensional generalizations of Kolmogorov flow ⋮ New estimates of the stability of one-dimensional plane-parallel flows of a viscous incompressible fluid ⋮ Time dependent periodic Navier-Stokes flows on a two-dimensional torus ⋮ Asymptotic analysis of the attractors in two-dimensional Kolmogorov flow ⋮ Instability of unidirectional flows for the 2D \(\alpha\)-Euler equations ⋮ Nonlinear stability of a parabolic velocity profile in a plane periodic channel ⋮ Transitions in a stratified Kolmogorov flow ⋮ Instabilities in two-dimensional spatially periodic flows. Part I: Kolmogorov flow ⋮ Stability of the Kolmogorov flow and its modifications ⋮ Hopf bifurcation and transition of three-dimensional wind-driven Ocean circulation problem ⋮ Nonlinear instability for the Boussinesq equations with diabatic forcing ⋮ Formation of coherent structures in Kolmogorov flow with stratification and drag ⋮ An Example of Instability for the Navier–Stokes Equations on the 2–dimensional Torus ⋮ Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process ⋮ Vortices of large scale appearing in the 2D stationary Navier-Stokes equations at large Reynolds numbers ⋮ Lieb-Thirring inequalities on the torus ⋮ Stability of a class of axisymmetric flows of an incompressible liquid ⋮ Eddy viscosity of three-dimensional flow ⋮ On the generation of large-scale eddy-driven patterns: the average eddy model ⋮ Stationary structures near the Kolmogorov and Poiseuille flows in the 2d Euler equations ⋮ Nonlinear Dynamics of Laminar-Turbulent Transition in Generalized 3D Kolmogorov Problem for Incompressible Viscous Fluid at Symmetric Solution Subset ⋮ On the stability problem of stationary solutions for the Euler equation on a 2-dimensional torus ⋮ Qualitative analysis of dynamics in Kolmogorov's problem on a flow of a viscous incompressible fluid ⋮ Sustaining processes from recurrent flows in body-forced turbulence ⋮ On the stability and bifurcation of the non-rotating Boussinesq equation with the Kolmogorov forcing at a low Péclet number ⋮ Thermohaline layering on the microscale ⋮ Generation of vortices in an axisymmetric shear flow ⋮ Kolmogorov flow: Linear stability and energy transfers in a minimal low-dimensional model ⋮ Anatole Katok ⋮ On the smallness condition in linear inviscid damping: monotonicity and resonance chains ⋮ Condensates in thin-layer turbulence ⋮ Three-dimensional long-wave instability of unidirectional spatially periodic viscous flows ⋮ Instability of Equilibria for the Two-Dimensional Euler Equations on the Torus ⋮ Analysis of the Kolmogorov model with an asymptotic-preserving method ⋮ The two-dimensional Navier-Stokes equations with a large-scale instability of the Kuramoto-Sivashinsky type: Numerical exploration on the connection machine ⋮ Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere ⋮ Onset of filtration convection in a vibrating medium: The Brinkman model ⋮ On 2D Euler equations. I. On the energy–Casimir stabilities and the spectra for linearized 2D Euler equations ⋮ Stability of Kolmogorov flow in a viscoelastic liquid ⋮ Selection of quasi-stationary states in the Navier–Stokes equation on the torus ⋮ Rossby and drift wave turbulence and zonal flows: the Charney-Hasegawa-Mima model and its extensions ⋮ Instability for the Navier-Stokes equations on the 2-dimensional torus and a lower bound for the Hausdorff dimension of their global attractors ⋮ Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori ⋮ Nonlinear instability for the critically dissipative quasi-geostrophic equation ⋮ Testing of model equations for the mean dissipation using Kolmogorov flows ⋮ Large time behavior and asymptotic stability of the 2D Euler and linearized Euler equations ⋮ Nonlinear instability for the Navier-Stokes equations ⋮ Stability results for idealized shear flows on a rectangular periodic domain ⋮ On stability of secondary flows of a viscous fluid in unbounded space ⋮ Zonal jet creation from secondary instability of drift waves for plasma edge turbulence ⋮ Barotropic instability of a time-dependent parallel flow ⋮ On the Stability of Two-Dimensional Flows Close to the Shear ⋮ Bifurcation computations on an approximate inertial manifold for the 2D Navier-Stokes equations ⋮ Suppression of internal waves by thermohaline staircases ⋮ Bifurcations in a quasi-two-dimensional Kolmogorov-like flow ⋮ Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations ⋮ Low-Index Equilibrium and Multiple Period-Doubling Cascades to Chaos of Atmospheric Flow in Beta-Plane Channel ⋮ Transport and instability in driven two-dimensional magnetohydrodynamic flows ⋮ On pseudospectral bound for non-selfadjoint operators and its application to stability of Kolmogorov flows ⋮ On the generation of large-scale structures in a homogeneous eddy field ⋮ Long-time behavior of Navier-Stokes flow on a two-dimensional torus excited by an external sinusoidal force ⋮ Numerical simulation of the three-dimensional Kolmogorov flow in a shear layer ⋮ On the nonlinear theory of stability of periodic flows ⋮ Stability Theory of the 3-Dimensional Euler Equations ⋮ Control of baroclinic instability by submesoscale topography ⋮ Unnamed Item ⋮ Hopf bifurcation of the three-dimensional Navier-Stokes equations ⋮ Onset of chaotic Kolmogorov flows resulting from interacting oscillatory modes
This page was built for publication: Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid