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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Global wellposedness of defocusing critical nonlinear Schrödinger equation in the radial case
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by J. Bourgain PDF
J. Amer. Math. Soc. 12 (1999), 145-171 Request permission

Abstract:

We establish global wellposedness and scattering for the $H^{1}$- critical defocusing NLS in 3D \begin{equation*}iu_{t}+\Delta u - u|u|^{4}=0 \end{equation*} assuming radial data $\phi \in H^{s}$, $s\geq 1$. In particular, it proves global existence of classical solutions in the radial case. The same result is obtained in 4D for the equation \begin{equation*}iu_{t}+\Delta u -u|u|^{2} =0. \end{equation*}
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Additional Information
  • J. Bourgain
  • Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
  • MR Author ID: 40280
  • Email: bourgain@math.ias.edu
  • Received by editor(s): April 20, 1998
  • © Copyright 1999 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 12 (1999), 145-171
  • MSC (1991): Primary 35Q55, 35L15
  • DOI: https://doi.org/10.1090/S0894-0347-99-00283-0
  • MathSciNet review: 1626257