Acoustic Limit for the Boltzmann equation in Optimal Scaling
نویسندگان
چکیده
Based on a recent L-L framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions.
منابع مشابه
Acoustic Limit of the Boltzmann Equation: Classical Solutions
We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution Fε = μ+ε √ μfε to the rescaled Boltzmann equation in the acoustic time scaling ∂tFε + v·∇xFε = 1 ε Q(Fε, Fε) , inside a periodic box T, we establish the global-in-time uniform energy estimates of fε in ε and prove that fε converges strongly to f whose dynamics is governed by the acous...
متن کاملRemarks on the Acoustic Limit for the Boltzmann Equation
We improve in three ways the results of [6] that establish the acoustic limit for DiPerna-Lions solutions of Boltzmann equation. First, we enlarge the class of collision kernels treated to that found in [13], thereby treating all classical collision kernels to which the DiPernaLions theory applies. Second, we improve the scaling of the kinetic density fluctuations with Knudsen number from O( ) ...
متن کاملThe Maxwell-Stefan diffusion limit for a kinetic model of mixtures
We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit.
متن کاملHydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities
The hydrodynamic limit for the Boltzmann equation is studied in the case when the limit system, that is, the system of Euler equations contains contact discontinuities. When suitable initial data is chosen to avoid the initial layer, we prove that there exists a unique solution to the Boltzmann equation globally in time for any given Knudsen number. And this family of solutions converge to the ...
متن کاملDerivation of the Isotropic Diffusion Source Approximation (IDSA) for Supernova Neutrino Transport by Asymptotic Expansions
We present Chapman–Enskog and Hilbert expansions applied to the O(v/c) Boltzmann equation for the radiative transfer of neutrinos in core-collapse supernovae. Based on the Legendre expansion of the scattering kernel for the collision integral truncated after the second term, we derive the diffusion limit for the Boltzmann equation by truncation of Chapman–Enskog or Hilbert expansions with react...
متن کامل