Stability of nonconstant steady‐state solutions for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor

We consider the periodic problem for 2‐fluid nonisentropic Euler‐Poisson equations in semiconductor. By choosing a suitable symmetrizers and using an induction argument on the order of the time‐space derivatives of solutions in energy estimates, we obtain the global stability of solutions with exponential decay in time near the nonconstant steady‐states for 2‐fluid nonisentropic Euler‐Poisson equations. This improves the results obtained for models with temperature diffusion terms by using the pressure functions p^ν in place of the unknown variables densities n^ν.     

Global convergence of an isentropic Euler-Poisson system in $\R^+ \times \R^d$

We prove the global-in-time convergence of an Euler-Poisson system near a constant equilibrium state in the whole space $\R^d$, as physical parameters tend to zero. The result follows from the uniform global existence of smooth solutions by means of energy estimates together with compactness arguments. For this purpose, we establish uniform estimates for $\dive \,u$ and $\curle \,u$ instead of $\nabla u$.     

Quasi-neutral limit for the full Euler–Poisson system in one-dimensional space

In this paper, we consider the quasi-neutral limit of the full Euler–Poisson system in one-dimensional space when the Debye length tends to zero. Due to the observation that the full Euler–Poisson system is Friedrich symmetrizable, we can obtain uniform estimates by applying the pseudo-differential energy estimates. It is shown that for well-prepared initial data the strong solution of the full Euler–Poisson system converges strongly to the compressible Euler equations in small time interval.     

Global weak solutions for the Vlasov–Poisson system with a point charge

We study the dynamics of three‐dimensional Vlasov‐Poisson system in the presence of a point charge with attractive interaction. Compared to the repulsive interaction,we cannot get a priori conversation law. Nevertheless,we are able to obtain bound of kinetic energy by introducing a Lyapunov functional. Combining this result with the concept of Diperna‐Lions flow, we establish global existence of weak solutions for this system. Copyright © 2014 John Wiley & Sons, Ltd.     

Stationary solutions of Euler–Poisson equations for non‐isentropic gaseous stars

The motion of the self‐gravitational gaseous stars can be described by the Euler–Poisson equations. For some velocity fields and entropy functions that solve the conservation of mass and energy, we consider the existence of stationary solutions of Euler–Poisson equations. Under various restriction to the strength of velocity field, different assumptions on the isentropic function and adiabatic exponent, we get the existence, multiplicity and uniqueness of the stationary solutions to the Euler–Poisson system, respectively. Copyright © 2012 John Wiley & Sons, Ltd.     

Global well‐posedness of the 2D Euler‐Boussinesq system with stratification effects

This paper is concerned with the Cauchy problem of the two‐dimensional Euler–Boussinesq system with stratification effects. We obtain the global existence of a unique solution to this system without assumptions of small initial data in Sobolev spaces. Copyright © 2017 John Wiley & Sons, Ltd.     

Asymptotic growth bounds for the 3‐D Vlasov‐Poisson system with point charges

In this article, we consider the asymptotic behavior of the classical solution to the 3‐dimensional Vlasov‐Poisson plasma interacting repulsively with N point charges. The large time behavior in terms of diameters of its velocity‐spatial supports is improved to O(t^2/3+ϵ) for any ϵ>0.     

Global and blow‐up solutions for non‐linear degenerate parabolic systems

In this paper the degenerate parabolic system u_t=u(u_xx+av). vt=v(v_xx+bu) with Dirichlet boundary condition is studied. For , the global existence and the asymptotic behaviour (α₁=α₂) of solution are analysed. For , the blow‐up time, blow‐up rate and blow‐up set of blow‐up solution are estimated and the asymptotic behaviour of solution near the blow‐up time is discussed by using the ‘energy’ method. Copyright © 2003 John Wiley & Sons, Ltd.     

Stability of non‐constant steady‐state solutions for non‐isentropic Euler–Maxwell system with a temperature damping term

This work is concerned with the periodic problem for compressible non‐isentropic Euler–Maxwell systems with a temperature damping term arising in plasmas. For this problem, we prove the global in time existence of a smooth solution around a given non‐constant steady state with the help of an induction argument on the order of the mixed time‐space derivatives of solutions in energy estimates. Moreover, we also show the convergence of the solution to this steady state as the time goes to the infinity. This phenomenon on the charge transport shows the essential relation of the systems with the non‐isentropic Euler–Maxwell and the isentropic Euler–Maxwell systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Existence of nontrivial solutions for fractional Schrödinger‐Poisson system with sign‐changing potentials

In this paper, we consider the following fractional Schrödinger‐Poisson system where 0 < t ≤ α < 1, , and 4α+2t ≥3 and the functions V(x), K(x) and f(x) have finite limits as |x|→∞. By imposing some suitable conditions on the decay rate of the functions, we prove that the above system has two nontrivial solutions. One of them is positive and the other one is sign‐changing. Recent results from the literature are generally improved and extended.     

Global relaxation and nonrelativistic limit of nonisentropic Euler-Maxwell systems

The aim of this paper is to investigate smooth solutions to Cauchy (or periodic) problem for a nonisentropic Euler-Maxwell system with small parameters. For initial data close to constant equilibrium states, we prove the global-in-time convergence of the Euler-Maxwell system as parameters go to zero. The limit systems are the drift-diffusion system and the nonisentropic Euler-Poisson system, respectively.     

Poisson convergence in the restricted k‐partitioning problem

The randomized k‐number partitioning problem is the task to distribute N i.i.d. random variables into k groups in such a way that the sums of the variables in each group are as similar as possible. The restricted k‐partitioning problem refers to the case where the number of elements in each group is fixed to N/k. In the case k = 2 it has been shown that the properly rescaled differences of the two sums in the close to optimal partitions converge to a Poisson point process, as if they were independent random variables. We generalize this result to the case k > 2 in the restricted problem and show that the vector of differences between the k sums converges to a k ‐ 1‐dimensional Poisson point process. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

Optimal decay rate of the bipolar Euler–Poisson system with damping in dimension three

By rewriting a bipolar Euler–Poisson equations with damping into a Euler equation with damping coupled with a Euler–Poisson equation with damping and using a new spectral analysis, we obtain the optimal decay results of the solutions in L² norm. More precisely, the velocities u₁ and u₂ decay at the L²?rate , which is faster than the normal L²‐rate for the heat equation and the Navier–Stokes equations. In addition, the decay rates of the disparities of two densities ρ₁?ρ₂ and the disparity of two velocities u₁?u₂ could reach to and in L² norm, respectively. Copyright © 2015 John Wiley & Sons, Ltd.     

一类p-Ginzburg-Landau型方程解的整体收敛性

作者研究了一类p-Ginzburg-Landau型方程解的整体收敛性.通过建立正则化方程解的梯度的一致估计,最终证明了解在C^α意义下收敛.     

Stability and convergence of the spectral Galerkin method for the Cahn‐Hilliard equation

A spectral Galerkin method in the spatial discretization is analyzed to solve the Cahn‐Hilliard equation. Existence, uniqueness, and stabilities for both the exact solution and the approximate solution are given. Using the theory and technique of a priori estimate for the partial differential equation, we obtained the convergence of the spectral Galerkin method and the error estimate between the approximate solution u_N(t) and the exact solution u(t). © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Blow‐up of smooth solutions to the Navier–Stokes–Poisson equations

The main purpose of this paper is concerned with blow‐up smooth solutions to Navier–Stokes–Poisson (N‐S‐P) equations. First, we present a sufficient condition on the blow up of smooth solutions to the N‐S‐P system. Then we construct a family of analytical solutions that blow up in finite time. Copyright © 2010 John Wiley & Sons, Ltd.     

Initial layers and zero‐relaxation limits of multidimensional Euler–Poisson equations

In this paper, we consider zero‐relaxation limits for periodic smooth solutions of the time‐dependent Euler–Poisson system. For well‐prepared initial data, we construct an approximate solution by an asymptotic expansion up to any order. For ill‐prepared initial data, we construct initial layer corrections in an explicit way. In both cases, the asymptotic expansions are valid in a time interval independent of the relaxation time, and their convergence is justified by establishing uniform energy estimates. Copyright © 2012 John Wiley & Sons, Ltd.     

Global smooth solution to a coupled Schrödinger system in atomic Bose-Einstein condensates with two-dimensional spaces

We obtain the global smooth solution of a nonlinear Schrödinger equations in atomic Bose-Einstein condensates with two-dimensional spaces. By using the Galerkin method and a priori estimates, we establish the global existence and uniqueness of the smooth solution.     

Global regularity for a two‐dimensional nonlinear Boussinesq system

In this paper, we first utilize the vanishing diffusivity method to prove the existence of global quasi‐strong solutions and get some higher order estimates, and then prove the global well‐posedness of the two‐dimensional Boussinesq system with variable viscosity for H³ initial data. Copyright © 2016 John Wiley & Sons, Ltd.     

Convergence of numerical solutions for variable delay differential equations driven by Poisson random jump measure

We study the following stochastic differential delay equations driven by Poisson random jump measure