Semantic Scholar Open Access 2015 7 sitasi

Invariance of Gibbs measures under the flows of Hamiltonian equations on the real line

A. Suzzoni F. Cacciafesta

Lihat Sumber DOI

Abstrak

We prove that the Gibbs measures [Formula: see text] for a class of Hamiltonian equations written as [Formula: see text] on the real line are invariant under the flow of [Formula: see text] in the sense that there exist random variables [Formula: see text] whose laws are [Formula: see text] (thus independent from [Formula: see text]) and such that [Formula: see text] is a solution to [Formula: see text]. Besides, for all [Formula: see text], [Formula: see text] is almost surely not in [Formula: see text] which provides as a direct consequence the existence of global weak solutions for initial data not in [Formula: see text]. The proof uses Prokhorov’s theorem, Skorohod’s theorem, as in the strategy in [N. Burq, L. Thomann and N. Tzvetkov, Remarks on the Gibbs measures for nonlinear dispersive equations, preprint (2014); arXiv:1412.7499v1 [math.AP]] and Feynman–Kac’s integrals.

Topik & Kata Kunci

Mathematics

Penulis (2)

A. Suzzoni

F. Cacciafesta

Format Sitasi

APA MLA BibTeX

Suzzoni, A., Cacciafesta, F. (2015). Invariance of Gibbs measures under the flows of Hamiltonian equations on the real line. https://doi.org/10.1142/S0219199719500123

Akses Cepat

Lihat di Sumber doi.org/10.1142/S0219199719500123

Informasi Jurnal

Tahun Terbit: 2015
Bahasa: en
Total Sitasi: 7×
Sumber Database: Semantic Scholar
DOI: 10.1142/S0219199719500123
Akses: Open Access ✓