ON INTEGRABILITY UP TO THE BOUNDARY OF THE WEAK SOLUTIONS TO A NON-NEWTONIAN FLUID

This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equartions as ■The existence result of weak solutions can be get based on Galerkin approximation. With the linear operator B constructed by BOGOVSKII, we show that the density ■is square integrable up to the boundary.     

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS FOR A SEMI-LINEAR HEAT EQUATION WITH FRACTIONAL LAPLACIAN

In this paper,we are concerned with the existence and non-existence of global solutions of a semi-linear heat equation with fractional Laplacian.We obtain some extension of results of Weissler who considered the case α = 1,and h ≡ 1.     

LPS＇S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R3. We show that if0 T +∞ is the maximal time interval for the unique smooth solution u ∈ C∞([0, T), R3),then |u| + |▽d| /∈ Lq([0, T ], Lp(R3)), where p and q safisfy the Ladyzhenskaya-Prodi-Serrin's condition:3p+2q= 1 and p ∈(3, +∞].     

具有特殊扩散过程的反应扩散方程

本文考虑如下具有特殊扩散系数的化学反应扩散方程的整体解存在性、渐近性和局部解有限时间爆破,这里Ω是RN(N≥3)中的光滑有界区域,0∈Ω,1＜p＜N+2/N-2.     

Heisenberg群上四阶非线性方程特征值问题的正解

本文通过Leray-Schauder度,给出Heisenberg群上四阶非线性次椭圆方程特征值问题的正解的一些存在性结果.     

On the heat flow equation of surfaces of constant mean curvature in higher dimensions

In this paper, we consider the heat flow for the Hsystem with constant mean curvature in higher dimensions. We give sufficient conditions on the initial data such that the heat flow develops finite time singularity. We also provide a new set of initial data to guarantee the existence of global regular solution to the heat flow, that converges to zero in W 1,n with the decay rate t 2/(2-n) as time goes to infinity.     

THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION

We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent.There are three major ingredients in this paper.The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value.The second ingredient is the L^q(2 ≤q <∞) estimate of the global solution applying the Moser iteration,which allows us to show that any global solution is a classical solution...     

等熵可压Navier-Stokes-Poisson方程局部强解适定性

该文得到了三维情形等熵可压Navier-Stokes-Poisson方程局部强解的存在性、唯一性及稳定性. 重要的是,该文允许初始密度真空的存在. 首先用推广形式的Gronwall不等式得到了强解的局部存在性,然后得到了较弱条件下的唯一性,在证明唯一性的同时得到了稳定性.     

退缩抛物方程整体解渐近性与轨道有界性

本文研究形如 的退缩抛物方程整体解与平衡解之间的关系和轨道在Ｗ１,ｐ０（Ω）－中的有界性．这里面△＝ｄｉｖ（｜　ｕ｜ｐ－２ｕ）,１＜ｐ＜Ｎ,ｐ＜ｑ＜ｐ＝ｐＮ／Ｎ－ｐ,Ω是ＲＮ（Ｎ≥３）的中具有光滑边界的有界区域．     

具有特殊扩散过程的反应扩散方程

本文考虑如下具有特殊扩散系数的化学反应扩散方程的整体解存在性、渐近性和局部解有限时间爆破,这里Ω是ＲＮ（Ｎ≥３）中的光滑有界区域,０∈Ω,１＜Ｐ＜Ｎ＋２／Ｎ－２．