Blow-up solutions on a sphere for the 3D quintic NLS in the energy space

@inproceedings{Holmer2010BlowupSO,
  title={Blow-up solutions on a sphere for the 3D quintic NLS in the energy space},
  author={Justin Holmer and Svetlana Roudenko},
  year={2010}
}
  • Justin Holmer, Svetlana Roudenko
  • Published 2010
  • Mathematics
  • We prove that if u(t) is a log-log blow-up solution, of the type studied by Merle-Raphael [14], to the L critical focusing NLS equation i∂tu+∆u+|u|u = 0 with initial data u0 ∈ H(R) in the cases d = 1, 2, then u(t) remains bounded in H away from the blow-up point. This is obtained without assuming that the initial data u0 has any regularity beyond H(R). As an application of the d = 1 result, we construct an open subset of initial data in the radial energy space H rad(R) with corresponding… CONTINUE READING

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