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MSRI Summer Microprogram on Nonlinear Partial Differential Equations |
| July 23, 2007 to August 10, 2007 |
| Organized By: L. C. Evans (UC Berkeley, Chair), C. Gutierrez (Temple), C. Sogge (Johns Hopkins), D. Tataru (UC Berkeley) |
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| Return to Workshop Description |
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Around the 2D energy critical NLKG
Monday August 6, 2007
04:00PM - 05:00PM
Speakers:
Slim Ibrahim
Abstract:
In previous works, it was proposed that in two space dimension, the energy critical NLKG equations are with exponential nonlinearities. The criticality was then discussed with respect to the size of the Hamiltonian compared to 1.
In the first part of the talk, I will briefly review the results of global well-posedness in the sub and critical cases, and the ill-posenedss of the supercritical problem.
In the second part I will show that every global solution in the sub- and critical cases scatters.
The peculiarity of this type of equations is that the Strichartz norms give time-local control of the nonlinearity which is not uniform as the energy tends to 1, and in the critical case (where the energy = 1), it is not a priori uniform in time even for a fixed solution.
The latter result is a joint work with M. Majdoub, N. Masmoudi and K. Nakanishi.
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