Solutions to the non-cutoff Boltzmann equation in the grazing limit

Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit

In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collision limit. To this aim we derive a Fourier spectral method for the non cut-off Boltzmann equation in the spirit of [21, 23]. We show that the kernel modes that define the spectral method have the correct grazing collis...

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...

The Incompressible Navier-stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials

The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Inve...

On the Grazing Collision Limit for the Spatially Homogeneous Boltzmann Equation

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

We present the formulation of a conservative spectral scheme for Boltzmann collision operators with anisotropic scattering mechanisms to model grazing collision limit regimes approximating the solution to the Landau equation in space homogeneous setting. The scheme is based on the conservative spectral method of Gamba and Tharkabhushanam [17, 18]. This formulation is derived from the weak form ...