相关论文: Stabilization and blow-up in the relativistic mode…

In this work, we study the behavior of blow-up solutions to the multidimensional restricted Euler--Poisson equations which are the localized version of the full Euler--Poisson system. We provide necessary conditions for the existence of…

In this article, we are interested in studying the Cauchy problems for nonlinear damped wave equations and their systems on a weighted graph. Our main purpose is two-fold, namely, under certain conditions for volume growth of a ball and the…

This paper is concerned with the analysis of a mathematical model arising in plasma physics, more specifically in fusion research. It directly follows \cite{DHK1}, where the tri-dimensional analysis of a Vlasov-Poisson equation with finite…

In this paper we study the linear stability of relative equilibria in the Newtonian $n$-body problem from the viewpoint of electromagnetic systems. We first examine the effect of the ambient dimension on stability, starting from the…

The effects of radiation on the structure of shocks in a fully-ionized plasma are investigated by solving the steady-state fluid equations for ions, electrons, and radiation. The electrons and ions are assumed to have the same bulk velocity…

The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this…

Several new methods of numerical integration of Cauchy problems with blow-up solutions for nonlinear ordinary differential equations of the first- and second-order are described. Solutions of such problems have singularities whose positions…

In this paper we use formal asymptotic arguments to understand the stability proper- ties of equivariant solutions to the Landau-Lifshitz-Gilbert model for ferromagnets. We also analyze both the harmonic map heatflow and Schrodinger map…

In this article, we initiate the study of the Cauchy problem for the two-dimensional relativistic Euler equations in a low-regularity setting. By introducing good variables--a rescaled velocity, logarithmic enthalpy, and an appropriately…

We numerically study the stability of collisionless equilibria in the context of general relativity. More precisely, we consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in Schwarzschild and in maximal areal…

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel…

We prove shock formation for 3D Euler-Poisson system for electron fluid plasma. The shock solution we construct is of large initial data, also compactly supported during the lifespan. In addition, the blowup time and location can be…

We study the equilibration of a parton plasma in terms of its parton compositions and its state of thermalization. In studying the evolution of the plasma, one has to assume a small value of the strong coupling constant. This value is by no…

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided, by including high-order artificial collision operators of Lenard-Bernstein type. These…

We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the…

In the initial stage of the bottom-up picture of thermalization in heavy ion collisions, the gluon distribution is highly anisotropic which can give rise to plasma instability. This has not been taken account in the original paper. It is…

In this work, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly-coupled plasma from the Lenard-Balescu equation. With some minor…

The theoretical model by Sorasio et al. (2006) for the steady state Mach number of electrostatic shocks formed in the interaction of two plasma slabs of arbitrary density and temperature is generalized for relativistic electron and…

Inspired by the numerical evidence of a potential 3D Euler singularity \cite{luo2014potentially,luo2013potentially-2}, we prove finite time blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite…

This is Part II of our paper in which we prove finite time blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite energy and boundary. In Part I of our paper [ChenHou2023a], we establish an…