Invariant measure for the Klein-Gordon equation in a non periodic setting

Abstract

In this paper, we build a Gibbs measure for the 1d cubic Klein-Gordon equation on $\mathbb{R}$ with a decreasing non linearity, in the sense that the non linearity $f^3$ is multiplied by $\chi$ where $\chi$ is a sufficiently integrable non negative function. We prove that this equation is almost surely globally well-posed in $H_{\text{loc}}^{1/2-}$ with respect to this measure and that the measure is invariant under the flow of the equation.

35 pages

References in corpus (1)

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

Cited by in corpus (3)

• Randomization and the Gross-Pitaevskii hierarchy
• Invariance of Gibbs measures under the flows of Hamiltonian equations on the real line
• Invariant measures for the non-periodic two-dimensional Euler equation