Related papers: High-friction limit for bipolar Euler-Riesz system…
In the present paper, we study the diffusion limit of the classical solution to the unipolar Vlasov-Poisson-Boltzmann (VPB) system with initial data near a global Maxwellian. We prove the convergence and establish the convergence rate of…
We here investigate a modification of the compressible barotropic Euler system with friction, involving a fuzzy nonlocal pressure term in place of the conventional one. This nonlocal term is parameterized by $\epsilon$ > 0 and formally…
Due to extreme difficulties in numerical simulations of Euler-Maxwell equations, which are caused by the highly complicated structures of the equations, this paper concerns the simplification of Euler-Maxwell system through the…
In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation…
The Euler-Poisson (EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs two-dimensional EP equations is studied. The evolution of divergence is governed by the Riccati type…
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution…
The Euler-Poisson(EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs the flow's gradient is studied. The evolution of divergence is governed by the Riccati type equation…
This articles presents a simulation study of the applicability of the Rosenfeld entropy scaling to the systems which can not be approximated by effective hard spheres. Three systems are studied: Herzian spheres, Gauss Core Model and soft…
The goal of the present paper is to prove that if a weak limit of a consistent approximation scheme of compressible complete Euler system in the full space $ \mathbb{R}^d,\; d=2,3 $ is a weak solution of the system then eventually the…
We study a one-dimensional cross-diffusion system for two interacting populations on the torus, with a fast-diffusion law with exponent $0< \alpha\le 1$ and different external potentials. For arbitrary non-negative $L^{1}$ initial data with…
We discuss the problem of well-posedness of the compressible (barotropic) Euler system in the framework of weak solutions. The principle of maximal dissipation introduced by C.M. Dafermos is adapted and combined with the concept of…
In this paper we consider a large system of Bosons or Fermions. We start with an initial datum which is compatible with the Bose-Einstein, respectively Fermi-Dirac, statistics. We let the system of interacting particles evolve in a…
In the paper, we consider a multi-dimensional bipolar hydrodynamic model from semiconductor devices and plasmas. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. We show…
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…
A reduced drift-diffusion (Smoluchowski-Poisson) equation is found for the electric charge in the high-field limit of the Vlasov-Poisson-Fokker-Planck system, both in one and three dimensions. The corresponding electric field satisfies a…
This work is a continuation of our papers from the last couple of years on the Casimir friction for a pair of particles at low relative velocity. The new element in the present analysis is to allow the media to be dense. Then the situation…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
The dynamics of interacting particles in orbital magnetic fields are notoriously difficult to study, as this physics is inherently connected to electronic correlations in two-dimensional systems, for which no straightforward theoretical…
Here we investigate global strong solutions for a class of partially dissipative hyperbolic systems in the framework of critical homogeneous Besov spaces. Our primary goal is to extend the analysis of our previous paper [10] to a functional…
We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche's method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of…