Invariant Gibbs Measures and a.s. Global Well-Posedness for Coupled KdV Systems

Abstract

We continue our study of the well-posedness theory of a one-parameter family of coupled KdV-type systems in the periodic setting. When the value of a coupling parameter α\in (0, 4) \setminus 1, we show that the Gibbs measure is invariant under the flow and the system is globally well-posed almost surely on the statistical ensemble, provided that certain Diophantine conditions are satisfied.

19 pages. To appear in Diff. Integ. Eqns

References in corpus (1)

• Sharp Global well-posedness for KdV and modified KdV on $\mathbb{R}$ and $\T$

Cited by in corpus (15)

• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
• Invariance of the white noise for KdV
• Invariance of white noise for KdV on the line
• Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two
• Solving the 4NLS with white noise initial data
• Invariant Gibbs Measure for 3D NLW in Infinite Volume
• Two Dimensional NLS Equation With Random Radial Data
• White noise for KdV and mKdV on the circle
• Invariant measure for the Klein-Gordon equation in a non periodic setting
• Nonlinear traveling waves for the skeleton of the Madden-Julian oscillation
• Random data Cauchy problem for a generalized KdV equation in the supercritical case
• Analysis on an extended Majda--Biello system
• Gibbs measure dynamics for the fractional NLS
• Gibbs measure for the periodic derivative nonlinear Schrödinger equation
• The Cauchy problem for the generalized KdV equation with rough data and random data