Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics
Department of Mathematics, University of California, Irvine, CA, 92697, USA.
2 Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA.
Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. We 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 for all domain aspect ratios, including the case of three wave resonances which yield nonlinear " 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.
Mathematics Subject Classification: 76D05 / 76D50 / 76U05 / 86A10
Key words: Fast singular oscillating limits / three-dimensional Navier-Stokes equations / primitive equations for geophysical fluid flows.
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