Global regularity of 3D rotating Navier-Stokes equations for resonant domains

A. Babin, Alex Mahalov, B. Nicolaenko

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear 2 1/2-dimensional limit equations; smoothness assumptions are the same as for local existence theorems. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems.

Original languageEnglish (US)
Pages (from-to)51-57
Number of pages7
JournalApplied Mathematics Letters
Volume13
Issue number4
StatePublished - May 2000

Fingerprint

Global Regularity
Navier Stokes equations
Rotating
Navier-Stokes Equations
Aspect ratio
Regular Solution
Local Existence
Bootstrapping
Boundary conditions
Decomposition
Free Boundary
Convergence Theorem
Aspect Ratio
Existence Theorem
Global Existence
Smoothness
Regularity
Decompose
Interval

Keywords

  • Resonances
  • Rotation
  • Three-dimensional Navier-Strokes equations

ASJC Scopus subject areas

  • Computational Mechanics
  • Control and Systems Engineering
  • Applied Mathematics
  • Numerical Analysis

Cite this

Global regularity of 3D rotating Navier-Stokes equations for resonant domains. / Babin, A.; Mahalov, Alex; Nicolaenko, B.

In: Applied Mathematics Letters, Vol. 13, No. 4, 05.2000, p. 51-57.

Research output: Contribution to journalArticle

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