Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics

Anatoli Babin, Alex Mahalov, Basil Nicolaenko

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. VVe prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter N). This uniform existence is proven for periodic or stress-free boundary conditions tor all domain aspect ratios, including the case of three wave resonances which yield nonlinear "21/2 dimensional" limit equations for N → +∞; smoothness assumptions are the same as for local existence theorems, that is initial data in Hα, α ≥ 3/4. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D "primitive" Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit resonant equations and convergence theorems.

Original languageEnglish (US)
Pages (from-to)201-222
Number of pages22
JournalMathematical Modelling and Numerical Analysis
Issue number2
StatePublished - 2000


  • Fast singular oscillating limits
  • Primitive equations for geophysical fluid flows
  • Three-dimensional Navier-Stokes equations

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Modeling and Simulation
  • Computational Mathematics
  • Applied Mathematics


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