Global dynamics beyond the ground state energy for nonlinear dispersive equations
Nakanishi, Kenji
Journées équations aux dérivées partielles, (2012), p. 1-6 / Harvested from Numdam
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This is a brief introduction to the joint work with Wilhelm Schlag and Joachim Krieger on the global dynamics for nonlinear dispersive equations with unstable ground states. We prove that the center-stable and the center-unstable manifolds of the ground state solitons separate the energy space by the dynamical property into the scattering and the blow-up regions, respectively in positive time and in negative time. The transverse intersection of the two manifolds yields nine sets of global dynamics, which include stable transition from blow-up to scattering and vice versa.

Publié le : 2012-01-01
DOI : https://doi.org/10.5802/jedp.91
Classification:  35L70,  35Q55 
@article{JEDP_2012____A8_0,
     author = {Nakanishi, Kenji},
     title = {Global dynamics beyond the ground state energy for nonlinear dispersive equations},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2012},
     pages = {1-6},
     doi = {10.5802/jedp.91},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2012____A8_0}
}

Nakanishi, Kenji. Global dynamics beyond the ground state energy for nonlinear dispersive equations. Journées équations aux dérivées partielles,  (2012), pp. 1-6. doi : 10.5802/jedp.91. http://gdmltest.u-ga.fr/item/JEDP_2012____A8_0/

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