Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Tuesday, February 12, 2002 - 2:00pm - 3:00pm
Keller 3-180
Alex Mahalov (Arizona State University)
Fast singular oscillating limits of the three-dimensional primitive equations for stably stratified rotating 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). This uniform existence is proven for all domain aspect ratios, including the case of all three wave resonances in the limit resonant equations; smoothness assumptions for initial data are the same as for local existence theorems, that is initial data in Hs, s > 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 strong convergence theorems. Algebraic geometry of resonant Poincare curves is also used to obtain regularity results in generic cases for solutions of 3D Euler primitive equations.