PDE Real Analysis Seminar Fast Singular Oscillating Limits of Hydrodynamic PDEs: application to 3D Euler, Navier-Stokes and MHD equations

2007-01-17 10:30 - 2007-01-17 11:30
Graduate School of Mathematical Sciences the University of Tokyo, Room #056
Professor Alex Mahalov (Arizona State University)
Methods of harmonic analysis and dispersive propertiesare applied to 3d hydrodynamic equations to obtain long-time and/orglobal existence results to the Cauchy problem for special classes of 3dinitial data. Smoothness assumptions for initial data are the same as inlocal existence theorems. Techniques for fast singular oscillatinglimits are used and large and/or infinite time regularity is obtained bybootstrapping from global regularity of the limit equations. The lattergain regularity from 3d nonlinear cancellation of oscillations.Applications include Euler, Navier-Stokes, Boussinesq and MHD equations,in infinite, periodic and bounded cylindrical domains.