Invariance of the Gibbs measure for the periodic quartic gKdV

Series: 
Stochastics Seminar
Thursday, January 31, 2013 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
IMA
The periodic generalized Korteweg-de Vries equation (gKdV) is a canonical dispersive partial differential equation with numerous applications in physics and engineering.  In this talk we present invariance of the Gibbs measure under the flow of the gauge transformed periodic quartic gKdV.  The proof relies on probabilistic arguments which exhibit nonlinear smoothing when the initial data are randomized.  As a corollary we obtain almost sure global well-posedness for the (ungauged) quartic gKdV at regularities where this PDE is deterministically ill-posed.