GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE NON-ISOTHERMAL NEMATIC LIQUID CRYSTALS IN 2D

In this article, we prove the global existence of weak solutions to the nonisothermal nematic liquid crystal system on T2, on the basis of a new approximate system which is different from the classical Ginzburg-Landau approximation. Local in space energy inequalities are employed to recover the estimates on the second order spatial derivatives of the director fields locally in time, which cannot be derived from the basic energy balance.It is shown that these weak solutions satisfy the temperature equation, and also the total energy equation but away from at most finite many "singular" times, at which the energy concentration occurs and the director field losses its second order derivatives.     

现代数学的最新趋势

今天和大家来谈谈现代数学的发展趋势．这个题目很大,我是不适合就这样的题目做报告．但是既然同学们需要,我就这个题目和同学们作一个探讨和交流．下面我将自己对数学各学科将来发展的一些粗浅想法,结合国内外同行对数学现状、当前国际上数学的发展趋势的理解,来展开我的报告.     

反应扩散方程Fife引理的一点注记及其应用

本文主要解决了P.C.Fife教授在北京讲学期间提出的一个问题.在反应扩散方程的初边值问题解的唯一性和稳定性的讨论中,P.C.Fife提出了一个很有用的基本引理,本文在减弱条件后仍得到了同样结果,并且给出这个结果的一些应用.     

THE TUBULAR CATALYST REACTOR AND THE ROBIN PROBLEM

In this paper,the model of chemical reaction experiments on a tubular catalyst reactor isdiscussed.We obtain the existence of the solution and discuss its uniqueness.Furthermore,in view ofmathematical interest,we also consider the Robin problem for this nonlinear system.     

ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS

In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].