| Advanced Course on PDEs 2006 |
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"High-Frequency limits of Hydrodynamic Models:
application to 3D Euler, Navier-Stokes and MHD equations"
Professor Basil Nicolaenko Arizona State University |
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Brescia - Italy May 15 - 17, 2006 |
| The course will be concentrated (10 hours in total) in 3 days (2+4+4), according to the following timetable: |
| Monday 15/05/06 | 14.30 - 16.30 | |
| Tuesday 16/05/06 | 10.30 - 12.30 | 14.30 - 16.30 |
| Wednesday 17/05/06 | 10.30 - 12.30 | 14.30 - 16.30 |
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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 both infinite, periodic and bounded cylindrical domains. |
Sponsors:
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