Invariant measures for the Nonlinear Schrodinger equation on the disc
Nikolay Tzvetkov
Abstract
We study Gibbs measures invariant under the flow of the NLS on the unit disc of 2. For that purpose, we construct the dynamics on a phase space of limited Sobolev regularity and a wighted Wiener measure invariant by the NLS flow. The density of the measure is integrable with respect to the Wiener measure for sub cubic nonlinear interactions. The existence of the dynamics is obtained in Bourgain spaces of low regularity. The key ingredient are bilinear Strichartz estimates for the free evolution. The bilinear effect in our analysis results from simple properties of the Bessel functions and estimates on series of Bessel functions.
Create a lesson
Related papers
Monotonicity of the propagation speed with respect to the diffusion in a Lotka-Volterra competition-diffusion system
Cyrille Kenne
Sign-preserving solutions to the Tzitzéica equation on lattice graphs
Pengxiu Yu, Yiping Zhang
Concavity and other properties of the entropy on manifolds
Xuenan Fu, Juanling Lu, Qi S. Zhang
The Higher-Dimensional Nitsche Conjecture: Sharp Bounds and Rigidity
Bin Deng, Jiahuan Li, Yilu Liu et al.
The complete spectrum of the linearized p-Laplacian at a Sobolev extremal
Yitian Zhang
Rigidity and existence of Busemann profiles for the Allen--Cahn equation on Cartan--Hadamard manifolds
Luis Eduardo Osorio-Acevedo, Álvaro Jaramillo