Related papers: Acoustic Limit for the Boltzmann equation in Optim…
We use some new nonlinear estimates found in \cite {LM} to improve the results of \cite{GL} that establish the acoustic limit for DiPerna-Lions solutions of Boltzmann equation in three ways. First, we enlarge the class of collision kernels…
We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution $F_\varepsilon=\mu +\varepsilon \sqrt{\mu}f_\varepsilon$ to the rescaled Boltzmann equation in the acoustic time scaling…
The convergence of the Boltzmann equaiton to the compressible Euler equations when the Knudsen number tends to zero has been a long standing open problem in the kinetic theory. In the setting of Riemann solution that contains the generic…
In [L. Liu and S. Jin, Multiscale Model. Simult., 16, 1085-1114, 2018], spectral convergence and long-time decay of the numerical solution towards the global equilibrium of the stochastic Galerkin approximation for the Boltzmann equation…
In this paper, we establish the global in time hydrodynamic limit of Boltzmann equation to the planar rarefaction wave of compressible Euler system in three dimensional space $x\in\mathbb{R}^3$ for general collision kernels. Our approch is…
In this paper, we prove the compressible Euler limit from the Boltzmann equation with hard sphere collisional kernel and complete diffusive boundary condition in half-space by employing the Hilbert expansion which includes interior and…
Although the compressible fluid limit of the Boltzmann equation with cutoff has been well investigated in [6] and [13], it still remains largely open to obtain analogous results in case of the angular non-cutoff or even in the grazing limit…
In this paper, we study the hydrodynamic and acoustic limit from Boltzmann equations for two species gas mixture with potential $\gamma \in \left(-3, 1\right]$. % in the whole space $(x \in \mathbb{R}^3)$.Here the particle masses are…
This paper justifies the compressible Euler and acoustic limits from quantum Boltzmann equation with Fermi-Dirac statistics (briefly, BFD) rigorously. This limit was formally derived in Zakrevskiy's thesis \cite{Zakrevskiy} by moment…
In the present paper, we concern the hydrodynamic limit of Boltzmann equation with specular reflection boundary condition in a two-dimensional disk to the compressible Euler equations. Due to the non-zero curvature and non-zero tangential…
We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear…
In this paper, we deal with (angular cut-off) Boltzmann equation with soft potential ($-3<\gamma<0$). In particular, we construct a unique global solution in $L^\infty_{x,v}$ which converges to global equilibrium asymptotically provided…
The study of hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to appearance of the viscous and Knudsen boundary layers. In this paper, the hydrodynamic limit from the Boltzmann equation with…
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…
We consider a linear Boltzmann equation that arises in a model for quantum friction. It describes a particle that is slowed down by the emission of bosons. We study the stochastic process generated by this Boltzmann equation and we show…
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…
We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in…
We consider the Boltzmann equations with cutoff collision kernels in bounded domains. For the initial data with finite physical bounds, we prove the existence of global-in-time renormalized solutions in the sense of DiPerna-Lions endowed…
We establish the incompressible low--Mach/high--Reynolds limit for the Boltzmann equation for a broad class of initial data, without recourse to any asymptotic expansion. Exploiting the local Maxwellian manifold and the macro--micro…
We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some…