The normal form of the Navier-Stokes equations in suitable normed spaces

DOI10.1016/j.anihpc.2008.09.003zbMath1179.35212OpenAlexW2050362081MaRDI QIDQ732514

Mohammed Ziane, Ciprian Foias, Luan Thach Hoang, Eric J. Olson

Publication date: 9 October 2009

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/78907

zbMATH Keywords

asymptotic expansionnormal formslong time dynamicsNavier-Stokesnormalization map

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Applications of functional analysis to differential and integral equations (46N20)

Related Items (10)

Asymptotic expansions for the Lagrangian trajectories from solutions of the Navier-Stokes equations ⋮ Asymptotic expansions in time for rotating incompressible viscous fluids ⋮ Asymptotic expansions in a general system of decaying functions for solutions of the Navier-Stokes equations ⋮ Generic properties of the spectrum of the Stokes system with Dirichlet boundary condition in \(\mathbb{R}^3\) ⋮ Asymptotic integration of Navier-Stokes equations with potential forces. II: An explicit Poincaré-Dulac normal form ⋮ NAVIER AND STOKES MEET POINCARÉAND DULAC ⋮ Infinite series asymptotic expansions for decaying solutions of dissipative differential equations with non-smooth nonlinearity ⋮ Asymptotic expansion for solutions of the Navier-Stokes equations with non-potential body forces ⋮ Asymptotic expansions with exponential, power, and logarithmic functions for non-autonomous nonlinear differential equations ⋮ Long-time asymptotic expansions for Navier-Stokes equations with power-decaying forces

Cites Work

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• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Linearization and normal form of the Navier-Stokes equations with potential forces
• Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
• Global stability of large solutions to the 3D Navier-Stokes equations
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• Remarques à propos du comportement, lorsque $t\to+\infty$, des solutions des équations de Navier-Stokes associées à une force nulle
• On the helicity in 3D-periodic Navier-Stokes equations I: the non-statistical case
• On the solutions to the normal form of the Navier-Stokes equations

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