该项目主要结合格林函数法，调和分析法，椭圆型偏微分方程及分数阶拉普拉斯算子的相关理论研究带非完全耗散结构或非局部算子的发展方程。具体包括：①利用格林函数高低频分解结合解的高低频分解构造有效能量泛函考虑非完全耗散结构，特别是由零特征值引起衰减性缺失给能量估计带来新困难的发展方程，得到解的存在性与大时间行为。②利用“近似格林函数”结合椭圆方程相关理论及加权能量估计考虑二维的包含由Poisson方程产生非局部的电场项的电磁流体模型非常数平衡态小扰动解的存在性和大时间行为。与三维情形相比较，二维是Poisson方程临界情形，会有本质的困难。③利用分数阶算子的多种定义及其相应性质，以及傅里叶分频法考虑分数阶耗散的发展方程解的存在性和大时间行为。④利用实分析与复分析，傅里叶分频法再结合格林函数法研究正则性缺失的或含非局部项的发展方程解的大时间行为，特别是逐点估计。

In this research, we study some evolution equations with partial dissipation or nonlocal terms by using methods of Green functions, Fourier splitting method, theories of elliptic equations and fractional Laplace operators. First, by using Fourier splitting method together with Green functions, we obtain global existence and large time behavior for some evolution equations with partial dissipation, especially for the equations with null eigenvalue, which will bring worse decay rate and new difficulties to derive energy estimates. Second, we study global existence and large time behaviors for electromagnetic field equations (contain a nonlocal electric field arising from the Poisson equation）when the initial perturbation for non-constant equilibrium state is small. Notice that the Poisson equation in dimension two is the critical case, thus there exist some essential difficulties compared with the previous works in dimension three. Third, we obtain the global existence and large time behavior of the solutions for some fluid models with fractional dissipation by using different definitions of the fractional Laplace operators and their propositions together with Fourier splitting method. Finally, we consider large time behaviors and pointwise estimates for regularity-loss evolution equations or evolution equations with non-local terms by using real analysis combining with complex analysis, and Fourier splitting method.