2025/09/25 by Elokhin, Alexey
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2509.21604
In rigorous study of stochastic models for the wave turbulence theory and R. Peierls's kinetic theory for the thermal conductivity in solids, analysis of integrals of the form ∫M (FωM)/(Ω2 + ν2Γ2) and ∫M \fracFcos(ν-1Ω)ωMΩ2 + ν2Γ2 plays a crucial role, where ν>0 is a small parameter, M is a closed Riemannian manifold with volume form ωM, and the functions Γ> 0, F, Ω are sufficiently smooth. We investigate the asymptotic behavior of the integrals in the limit ν→ 0. This work continues studies [Kuksin' 17, Dymov' 23], in which the authors considered similar integrals for the case M=ℝd when the function Ω is Morse. We significantly weaken the latter assumption, which played an important role in the aforementioned works. This makes the obtained results applicable to the problem of rigorous justification of R. Peierls's kinetic theory.