The 30th PDE Real Analysis Seminar
(COE Partner Seminar, Department of Mathematics, Hokkaido University )
Outline
- Organizers :
-
H.Arai (University of Tokyo), Y.Giga (University of Tokyo/Hokkaido University)
- Board Members :
- H.Ishii (Waseda.U), T.Kawazoe (Keio.U), N.Kenmochi (Chiba.U), M.Sakai (Tokyo Metropolitan.U), Y.Shibata (Waseda.U), K.Mochizuki (Chuo.U), A.Miyachi(Tokyo Woman's Christian.U), M.Yamamoto (University of Tokyo)
- Period :
- January 17, 2007 (Wednesday) 10:30-11:30
- Place :
- Graduate School of Mathematical Sciences the University of Tokyo, Room #056
- Programme :
-
- Alex Mahalov (Arizona State University)
- TITLE:
- Fast Singular Oscillating Limits of Hydrodynamic PDEs: application to 3D Euler, Navier-Stokes and MHD equations
- ABSTRACT:
- Methods of harmonic analysis and dispersive properties are applied to 3d hydrodynamic equations to obtain long-time and/or global existence results to the Cauchy problem for special classes of 3d initial data. Smoothness assumptions for initial data are the same as in local existence theorems. Techniques for fast singular oscillating limits are used and large and/or infinite time regularity is obtained by bootstrapping from global regularity of the limit equations. The latter gain regularity from 3d nonlinear cancellation of oscillations. Applications include Euler, Navier-Stokes, Boussinesq and MHD equations, in infinite, periodic and bounded cylindrical domains.
