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Seminários do IMPA

Análise / Equações Diferenciais Parciais

Título
On a new approach to scattering for dispersive equations
Expositor
Luccas Campos

Universidade Federal de Minas Gerais (Brazil) and Florida International University (USA)
Data
Quinta-feira, 20 de fevereiro de 2020, 15:30
Local
Sala 232
Resumo

The concentration-compactness-rigidity method, pioneered by Kenig and Merle, has become standard in the study of global well-posedness and scattering in the context of dispersive and wave equations. Albeit powerful, it requires building some heavy machinery in order to obtain the desired space-time bounds.

In this talk, we present a simpler method, based on Tao's scattering criterion and on Dodson-Murphy's Virial/Morawetz inequalities, first proved for the 3d cubic nonlinear Schrödinger (NLS) equation.
 
Tao's criterion is, in some sense, universal, and it is expected to work in similar ways for dispersive problems. On the other hand, the Virial/Morawetz inequalities need to be established individually for each problem, as they rely on monotonicity formulae.
 
This approach is versatile, as it was shown to work in the energy-subcritical setting for different nonlinearities, as well as for higher-order equations.