Invariant measures and the soliton resolution conjecture
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: SLMath: Eisenbud Auditorium
discrete NLS on a torus
ergodic components
soliton solutions
sub-critical mass
Birkhoff's ergodicity theorem
existence of global solutions
26A46 - Absolutely continuous real functions in one variable
35L03 - Initial value problems for first-order hyperbolic equations
14380
I will talk about the micro-canonical invariant measure for the discrete nonlinear Schrödinger equation on a torus in the mass-subcritical regime, and prove that a random function drawn from this measure is close to the ground state soliton with high probability. This proves that “almost all” ergodic components of this flow have the property of convergence to a soliton in the long run, which is a statistical variant of what is sometimes called the soliton resolution conjecture
Chatterjee_Notes
|
Download |
14380
H.264 Video |
14380.mp4
|
Download |
Please report video problems to itsupport@slmath.org.
See more of our Streaming videos on our main VMath Videos page.