---
res:
  bibo_abstract:
  - 'We consider the minimal mass m0 required for solutions to the mass-critical nonlinear
    Schrödinger (NLS) equation iut + Δu = μ|u|^4/d u to blow up. If m0 is finite,
    we show that there exists a minimal-mass solution blowing up (in the sense of
    an infinite spacetime norm) in both time directions, whose orbit in  is compact
    after quotienting out by the symmetries of the equation. A similar result is obtained
    for spherically symmetric solutions. Similar results were previously obtained
    by Keraani, [Keraani S.: On the blow-up phenomenon of the critical nonlinear Schrödinger
    equation. J. Funct. Anal. 235 (2006), 171–192], in dimensions 1, 2 and Begout
    and Vargas, [Begout P., Vargas A.: Mass concentration phenomena for the L2-critical
    nonlinear Schrödinger equation, preprint], in dimensions d ≥ 3 for the mass-critical
    NLS and by Kenig and Merle, [Kenig C., Merle F.: Global well-posedness, scattering,
    and blowup for the energy-critical, focusing, non-linear Schrödinger equation
    in the radial case, preprint], in the energy-critical case. In a subsequent paper
    we shall use this compactness result to establish global existence and scattering
    in  for the defocusing NLS in three and higher dimensions with spherically symmetric
    data.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Terence
      foaf_name: Tao, Terence
      foaf_surname: Tao
  - foaf_Person:
      foaf_givenName: Monica
      foaf_name: Visan, Monica
      foaf_surname: Visan
      foaf_workInfoHomepage: http://www.librecat.org/personId=056daca0-b8d1-11f0-964f-f91054abf8ca
  - foaf_Person:
      foaf_givenName: Xiaoyi
      foaf_name: Zhang, Xiaoyi
      foaf_surname: Zhang
  bibo_doi: 10.1515/forum.2008.042
  bibo_issue: '5'
  bibo_volume: 20
  dct_date: 2008^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0933-7741
  - http://id.crossref.org/issn/1435-5337
  dct_language: eng
  dct_publisher: De Gruyter@
  dct_title: Minimal-mass blowup solutions of the mass-critical NLS@
...