Uniform boundedness and long-time asymptotics for the two-dimensional Navier-Stokes equations in an infinite cylinder

DOI10.1007/s00021-014-0188-zzbMath1320.35258arXiv1402.6563OpenAlexW3105372287MaRDI QIDQ2355630

Siniša Slijepčević, Thierry Gallay

Publication date: 24 July 2015

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.6563

zbMATH Keywords

Navier-Stokes equationslong-time behaviorglobal existenceuniform bounds

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Shear flows and turbulence (76F10) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Viscous vortex flows (76D17)

Related Items (12)

Diffusive relaxation to equilibria for an extended reaction-diffusion system on the real line ⋮ On the growth of the support of positive vorticity for 2D Euler equation in an infinite cylinder ⋮ Stability of synchronization in dissipatively driven Frenkel-Kontorova models ⋮ Contour Dynamics and Global Regularity for Periodic Vortex Patches and Layers ⋮ Bounded solutions in incompressible hydrodynamics ⋮ Global well-posedness of the two-dimensional exterior Navier-Stokes equations for non-decaying data ⋮ Infinite energy solutions of the two-dimensional Navier–Stokes equations ⋮ On the large time \(L^\infty \)-estimates of the Stokes semigroup in two-dimensional exterior domains ⋮ Infinite energy solutions for dissipative Euler equations in \(\mathbb{R}^2\) ⋮ Local energy weak solutions for the Navier-Stokes equations in the half-space ⋮ Vanishing viscosity limits for axisymmetric flows with boundary ⋮ Variational construction of positive entropy invariant measures of Lagrangian systems and Arnold diffusion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Distribution of energy and convergence to equilibria in extended dissipative systems
• The Navier-Stokes equations with initial data in uniformly local \(L^p\) spaces.
• A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
• Heat kernel upper bounds on a complete non-compact manifold
• The uniqueness of nondecaying solutions for the Navier-Stokes equations
• Dynamical properties of spatially non-decaying 2D Navier-Stokes flows with Kolmogorov forcing in an infinite strip
• Ultracontractivity and Nash type inequalities
• On isoperimetric profiles of product spaces
• Infinite-energy solutions for the Navier-Stokes equations in a strip revisited
• Infinite energy solutions for damped Navier-Stokes equations in \({\mathbb{R}^2}\)
• A remark on \(L^{\infty}\) solutions to the 2-D Navier-Stokes equations
• Serfati solutions to the 2D Euler equations on exterior domains
• Energy Bounds for the Two-Dimensional Navier-Stokes Equations in an Infinite Cylinder
• LINEAR PARABOLIC EQUATIONS IN LOCALLY UNIFORM SPACES
• Continuity of Solutions of Parabolic and Elliptic Equations
• SPATIALLY NONDECAYING SOLUTIONS OF THE 2D NAVIER-STOKES EQUATION IN A STRIP
• Bounds for the fundamental solution of a parabolic equation
• Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity
• Energy flow in formally gradient partial differential equations on unbounded domains

This page was built for publication: Uniform boundedness and long-time asymptotics for the two-dimensional Navier-Stokes equations in an infinite cylinder