One-sided convergence in the Boltzmann-Grad limit

The periodic Lorentz gas is the dynamical system corresponding to the free motion of a point particle in a periodic system of fixed spherical obstacles of radius r centered at

In this work, we have derived the incompressible Euler equations from the Boltz- mann equation in the case of the initial boundary value problem, for a class of boundary conditions

Keywords: Boltzmann equation; spatially homogeneous; hard potentials; measure solutions; equilibrium; exponential rate of convergence; eternal solution; global-in-time

The main idea to prove the convergence of the solutions to the scaled Boltzmann- Fermi equation toward a solution of the incompressible Euler equation is to study the time evolution

They go back to Nishida [39] for the compressible Euler equation (this is a local in time result) and this type of proof was also developed for the incompressible Navier-Stokes

Uffink and Valente (2015) claim that neither the B-G limit, nor the ingoing configurations are responsible for the appearance of irreversibility. Their argu- ments are specific for

particles, strongly interacting at distance ε, the particle density approximates the solution to the Boltzmann equation when N → ∞ , ε → 0, in such a way that the collision

When T is a contraction in a Hilbert space, we show that the logarithmic Hausdorff dimension of the set of λ’s for which this series does not converge is at most 2 and give