On the rigorous ergodic theorem for a class of nonlinear Klein–Gordon wave propagations

We present a complete study of the ergodic theorem for the problem of nonlinear Klein–Gordon classical wave propagations through cylindrical measures, rigorous mathematical path integrals and the well-known Ruelle–Amrein–Georgescu–Enss (RAGE) theorem on the characterization of the continuous spectrum of self-adjoint operators.

FLOWS OF VISCOUS COMPRESSIBLE FLUIDS UNDER STRONG STRATIFICATION: INCOMPRESSIBLE LIMITS FOR LONG-RANGE POTENTIAL FORCES

We study the singular limit of the compressible Navier–Stokes system in the whole space ℝ3, where the Mach number and Froude number are proportional to a small parameter ε → 0. The central issue is the local decay of the acoustic energy proved by means of the RAGE theorem. The result is quite general and the proposed approach can be applied to a large variety of problems that concern propagation of acoustic waves in compressible fluids. In particular, the method can be used for showing stability of various numerical schemes based on the so-called hybrid methods.