Titulo: Nonradial blow-up solutions for the Zakharov system
Palestrante: Juan C. Cordero Ceballos (UNAL, Colômbia)
Local: Sala - C116
Resumo: We will show that there are nonradial solutions for the Zakharov equations, which have blow-up in finite time in the case of negative energy, due to a virial identity of momentum type. This solutions are standing waves for the Zakharov-Rubenchik system, so we give response to two questions proposed by F. Merle in .
 F. Merle, Blow-up results of virial type for Zakharov Equations, Communications in Mathematical Physics, 175, 433-455 (1996)
 J. C. Cordero, Supersonic limit for the Zakharov-Rubenchik system, Journal Differential Equations, 261 (2016), 5260-5288
 J. R. Quintero, J.C. Cordero, Instability of the standing waves for a Benney-Roskes/Zakharov-Rubenchik system and blow-up for the Zakharov equations, Discrete and Continuous Dynamical Systems Series B doi:10.3934/dcdsb.2019217