Fast singular oscillating limits and global regularity for the 3D primitive equations of geophysics
Local Smoothness of Weak Solutions to the Magnetohydrodynamics Equations via Blowup Methods
We demonstrate that there exist no self-similar solutions of the incompressible magnetohydrodynamics (MHD) equations in the space . This is a consequence of proving the local smoothness of weak solutions via blowup methods for weak solutions which are locally . We present the extension of the Escauriaza-Seregin-Sverak method to MHD systems.
Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics
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 ). This uniform existence is proven for periodic or stress-free boundary conditions for domain aspect ratios, including the case of three wave resonances which yield nonlinear " dimensional" limit equations...
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