JournalsjemsVol. 11 , No. 1DOI 10.4171/jems/143

Non-generic blow-up solutions for the critical focusing NLS in 1-D

  • Wilhelm Schlag

    University of Chicago, United States
  • Joachim Krieger

    EPFL, Lausanne, Switzerland
Non-generic blow-up solutions for the critical focusing NLS in 1-D cover

Abstract

We consider the L2-critical focussing nonlinear Schrödinger equation in 1+1-D. We demonstrate the existence of a large set of initial data close to the ground state soliton resulting in the pseudo-conformal type blow up behavior. More specifically, we prove a version of a conjecture of Perelman, establishing the existence of a co-dimension one stable blow up manifold in the measurable category.