Invariant Gibbs measures for the defocusing NLS on the real line

Add to your list(s) Download to your calendar using vCal

• Tadahiro Oh (Edinburgh)
• Monday 26 May 2014, 15:00-16:00
• CMS, MR13.

If you have a question about this talk, please contact .

In 1994, Bourgain constructed invariant Gibbs measures for NLS on the circle. Then, in 2000, he considered the limit of these invariant statistics, by taking larger and lager periods, and constructed unique solutions for the defocusing (sub-)cubic NLS on the real line. His result, however, focuses on the construction of solutions and does not discuss the limiting Gibbs measures on the real line or their invariance.

In this talk, we construct Gibbs measures for the defocusing NLS on the real line as a stationary diffusion process in x. Then, we show that these Gibbs measures are invariant for the defocusing (sub-)quintic NLS on the real line. We also discuss the limit Gibbs measures for the Dirichlet boundary value problem on the real line as well as the half line, allowing us to construct new rough solutions in these settings.

This is a joint work with Jeremy Quastel (University of Toronto) and Philippe Sosoe (Harvard University).

This talk is part of the Partial Differential Equations seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• CMS, MR13
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• My seminars
• Partial Differential Equations seminar
• School of Physical Sciences
• bld31

Note that ex-directory lists are not shown.