论文标题
半木星驱动的变分原理
Semi-martingale driven variational principles
论文作者
论文摘要
在最近为推导随机地球物理流体动力学模型的努力的带头上，我们提出了一个通用框架，可以通过半木星驱动的变异原理的概念将随机性引入变化原理，并限制组件变量与驱动半合作赛兼容。在此框架和相应的约束选择中，可以轻松地推导Euler-Poincare方程。我们表明，它们相应的确定性对应物是此类随机变异原理的特殊情况。此外，这是一个自然框架，使我们能够正确地表征不可压缩的随机流体模型中的压力项。只要与驾驶半木星兼容，其他一般约束也可以合并。
Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into variational principles through the concept of a semi-martingale driven variational principle and constraining the component variables to be compatible with the driving semi-martingale. Within this framework and the corresponding choice of constraints, the Euler-Poincare equation can be easily deduced. We show that their corresponding deterministic counterparts are particular cases of this class of stochastic variational principles. Moreover, this is a natural framework that enables us to correctly characterize the pressure term in incompressible stochastic fluid models. Other general constraints can also be incorporated as long as they are compatible with the driving semi-martingale.
