Remarks on global a priori estimates for the nonlinear Schrödinger equation

J. Colliander, M. Grillakis, N. Tzirakis

Research output: Contribution to journalArticlepeer-review


We present a unified approach for obtaining global a priori estimates for solutions of nonlinear defocusing Schrödinger equations with defocusing nonlinearities. The estimates are produced by contracting the local momentum conservation law with appropriate vector fields. The corresponding law is written for defocusing equations of tensored solutions. In particular, we obtain a new estimate in two dimensions. We bound the restricted L4t L t4 Lt4 Strichartz norm of the solution on any curve γ in ℝ2. For the specific case of a straight line we upgrade this estimate to a weighted Strichartz estimate valid in the full plane.

Original languageEnglish (US)
Pages (from-to)4359-4371
Number of pages13
JournalProceedings of the American Mathematical Society
Issue number12
StatePublished - Dec 2010

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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