相关论文: Boltzmann to Landau from the Gradient Flow Perspec…

We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows.

We consider a Fokker-Planck equation which is coupled to an externally given time-dependent constraint on its first moment. This constraint introduces a Lagrange-multiplier which renders the equation nonlocal and nonlinear. In this paper we…

We discuss the grazing collision limit of certain kinetic models of Bose-Einstein particles obtained from a suitable modification of the one- dimensional Kac caricature of a Maxwellian gas without cut-off. We recover in the limit a…

We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisions in the grazing regime, and happens to be a special…

Starting with the relativistic Boltzmann equation where the collision term was generalized to include gradients of the phase-space distribution function, we recently presented a new derivation of the equations for the relativistic…

It is known that in the parameters range $-2 \leq \gamma <-2s$ spectral gap does not exist for the linearized Boltzmann operator without cutoff but it does for the linearized Landau operator. This paper is devoted to the understanding of…

We derive approximate iterative analytical solutions of the non-extensive Boltzmann transport equation in the relaxation time approximation. The approximate solutions almost overlap with the exact solution for a considerably wide range of…

In this paper we prove new constructive coercivity estimates and convergence to equilibrium for a spatially non-homogeneous system of Landau equations with soft potentials. We show that the nonlinear collision operator conserves each…

We present a derivation of a Boltzmann equation for the QCD plasma, starting from the quantum field equations. The derivation is based on a gauge covariant gradient expansion which takes consistently into account all possible dependences on…

We present an exact solution of the relativistic Boltzmann equation for a system undergoing boost-invariant longitudinal and azimuthally symmetric transverse flow ("Gubser flow"). The resulting exact non-equilibrium dynamics is compared to…

We prove convergence of the gradient flow of the Ginzburg-Landau energy functional on a Riemann surface in the self-dual Bogomolny case, in Coulomb gauge. The proof is direct and makes use of the associated nonlinear first order…

We study the derivation of the spatially homogeneous Landau equation from the mean-field limit of a conservative $N$-particle system, obtained by passing to the grazing limit on Kac's walk in his program for the Boltzmann equation. Our…

In earlier work we showed that the particle displacement for the multidimensional periodic Lorentz gas, in the limit of low scatterer density (Boltzmann-Grad limit), satisfies a central limit theorem with superdiffusive scaling. The present…

Inspired by recent work on minimizers and gradient flows of constrained interaction energies, we prove that these energies arise as the slow diffusion limit of well-known aggregation-diffusion energies. We show that minimizers of…

Starting from Boltzmann equation with relaxation time approximation for the collision term and using Chapman-Enskog like expansion for distribution function close to equilibrium, we derive hydrodynamic evolution equations for the…

This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…

This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of…

We study a fuzzy Boltzmann equation, where collisions are delocalised and modulated by a spatial kernel. We show that as the spatial kernel converges to a delta distribution, the solutions to these equations converge to renormalised…

In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such…

A jump-diffusion process along with a particle scheme is devised as an accurate and efficient particle solution to the Boltzmann equation. The proposed process (hereafter Gamma-Boltzmann model) is devised to match the evolution of all…