论文标题
部分可观测时空混沌系统的无模型预测
Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations
论文作者
论文摘要
我们定义了三个空间维度的埃里克森方程的能量变化解决方案的概念。该解决方案概念比耗散解决方案更细，并且满足了弱的唯一性能。为了确定规律性的重量，能量变化解决方案的存在意味着衡量解决方案的存在，并且对于不同的选择，我们借助实施的，结构的实时时空离散化构建了能量变化的解决方案。进行计算研究以提供一些证据表明该算法的适用性。
We define the concept of energy-variational solutions for the Ericksen--Leslie equations in three spatial dimensions. This solution concept is finer than dissipative solutions and satisfies the weak-strong uniqueness property. For a certain choice of the regularity weight, the existence of energy-variational solutions implies the existence of measure-valued solutions and for a different choice, we construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm.
