Related papers: The Landau equation in a domain
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary…
The existence and stability of the Landau equation (1936) in a general bounded domain with a physical boundary condition is a long-outstanding open problem. This work proves the global stability of the Landau equation with the Coulombic…
This work deals with the Landau equation for very soft and Coulomb potentials near the associated Maxwellian equilibrium. We first investigate the corresponding linearized operator and develop a method to prove stability estimates of its…
In this article we study the well-posedness of the Boltzmann equation near its hydrodynamic limit on a bounded domain. We consider two types of domains, namely $C^2$ domains with Maxwell boundary conditions where the accommodation…
The existence and stability of collisional kinetic equation, especially non-cutoff Boltzmann equation, in bounded domain with physical boundary condition is longstanding open problem. This work proves the global stability of the Landau…
We study the degenerate linear Boltzmann equation inside a bounded domain with a generalized diffuse reflection at the boundary and variable temperature, including the Maxwell boundary conditions with the wall Maxwellian or heavy-tailed…
We prove the local-in-time well-posedness of the relativistic Vlasov-Maxwell-Landau system in a bounded domain $\Omega$ with the specular reflection condition. Our result covers the case when $\Omega$ is a non-convex domain, e.g., solid…
We prove global stability results of {\sl DiPerna-Lions} renormalized solutions for the initial boundary value problem associated to some kinetic equations, from which existence results classically follow. The (possibly nonlinear) boundary…
For the Landau-Poisson system with Coulomb interaction in $\R^3_x$, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close.
The existence theory for solutions to the Boltzmann equation in bounded domains has primarily been developed within uniformly bounded function classes, such as $L^{\infty}_{x,v}$, as in [Duan-Huang-Wang-Yang,2017], [Duan-Wang,2019],…
We establish the global-wellposedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external…
In rotationally symmetric domains, the Boltzmann equation with specular reflection boundary condition has a special type of equilibrium states called the rotational local Maxwellian which, unlike the uniform Maxwellian, has an additional…
We study steady Boltzmann equation in half-space, which arises in the Knudsen boundary layer problem, with diffusive reflection boundary conditions. Under certain admissible conditions and the source term decaying exponentially, we…
This work deals with the large time behaviour of the spatially homogeneous Landau equation with Coulomb potential. Firstly, we obtain a bound from below of the entropy dissipation $D(f)$ by a weighted relative Fisher information of $f$ with…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
We consider the Kinetic Fokker-Planck (FKP) equation in a domain with Maxwell reflection condition on the boundary. We establish the ultracontractivity of the associated semigroup and the hypocoercivity of the associated operator. We deduce…
Global well-posedness and exponential decay to equilibrium are proved for the homogeneous Landau equation from kinetic theory. The initial distribution is only assumed to be bounded and decaying sufficiently fast at infinity. In particular,…
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…
We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion…
We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near…