Related papers: Compressible Euler limit from Boltzmann equation w…
We consider a singular limit problem for the complete compressible Euler system in the low Mach and strong stratification regime. We identify the limit problem - the anelastic Euler system - in the case of well prepared initial data. The…
We derive the Boltzmann equation and the collision kernel for massive spin-1/2 particles, using the Wigner-function formalism and employing an expansion in powers of $\hbar$. The phase space is enlarged to include a variable related to the…
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…
In this paper we prove the strong and time-averaged strong convergence to equilibrium for solutions (with general initial data) of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. The assumption on the collision…
We consider the Cauchy problem with smooth data for compressible Euler equations in many dimensions and concentrate on two cases: solutions with finite mass and energy and solutions corresponding to a compact perturbation of a nontrivial…
Flows in which the primary features of interest do not rely on high-frequency acoustic effects, but in which long-wavelength acoustics play a nontrivial role, present a computational challenge. Integrating the entire domain with…
Liebmann's Theorem asserts that a compact, connected, convex surface with constant mean curvature (CMC) in the Euclidean space must be a totally umbilical sphere. In this article we extend Liebmann's result to hypersurfaces with boundary.…
This paper is a continuation of the works in \cite{Euler} and \cite{NS}, where the authors have established the global existence of smooth compressible flows in infinitely expanding balls for inviscid gases and viscid gases, respectively.…
We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain…
Under the diffusion scaling and a scaling assumption on the microscopic component, a non-classical fluid dynamic system was derived in \cite{BGLY} that is related to the system of ghost effect derived in \cite{Sone-2} in different settings.…
We study a space-fractional Stefan problem with the Dirichlet boundary conditions. It is a model that describes superdiffusive phenomena. Our main result is the existence of the unique classical solution to this problem. In the proof we…
The purpose of this paper consists in proposing a generalized solution for a porous media type equation on a half-line with Neumann boundary condition and prove a probabilistic representation of this solution in terms of an associated…
We prove a priori estimates for the compressible Euler equations modeling the motion of a liquid with moving physical vacuum boundary in an unbounded initial domain. The liquid is under influence of gravity but without surface tension. Our…
By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of…
A strong-coupling expansion for the phase boundary of the (incompressible) Mott insulator is presented for the bose Hubbard model. Both the pure case and the disordered case are examined. Extrapolations of the series expansions provide…
We are concerned with a time periodic supersonic flow through a bounded interval. This motion is described by the compressible Euler equation with a time periodic outer force. Our goal in this paper is to prove the existence of a time…
The purpose of this work is the study of solution techniques for problems involving fractional powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary conditions. These operators can be realized as the…
This article provides sharp constructive upper and lower bound estimates for the non-linear Boltzmann collision operator with the full range of physical non cut-off collision kernels ($\gamma > -n$ and $s\in (0,1)$) in the trilinear…
We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…
We consider the spatially inhomogeneous quantum Boltzmann equation for bosons with a singular collision kernel, the weak-coupling limit of a large system of Bose-Einstein particles interacting through inverse power law. Global…