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Symplectic non-squeezing for the cubic NLS on R^2

New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 19, 2015 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Monica Visan (University of California, Los Angeles)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Hamiltonian PDE

  • Gromov

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14370

Abstract

We prove that the flow of the mass-critical NLS in two dimensions cannot squeeze a ball in $L^2$ into a cylinder of lesser radius.  This is a PDE analogue of Gromov's non-squeezing theorem for an infinite-dimensional Hamiltonian PDE in infinite volume.  This is joint work with R. Killip and X. Zhang

Supplements
24932?type=thumb Visan_Notes 1.14 MB application/pdf Download
Video/Audio Files

14370

H.264 Video 14370.mp4 329 MB video/mp4 rtsp://videos.msri.org/data/000/024/544/original/14370.mp4 Download
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