随机变分方法在流体力学中的应用
Application of Stochastic Variational Method to Hydrodynamics
摘要：
本文将随机变分方法应用于理想流体的作用，导出了纳维-斯托克斯方程。在这种变分方法中，耗散的效果是实现作为波动耗散定理的直接后果。在前人工作\cite{kk1,kk2}的基础上，我们以更一般的形式对支持向量机的拉格朗日量进行参数化。所得方程的形式不变，但输运系数的定义有所改变。我们进一步讨论了支持向量机的制定使用的哈密顿量，并表明，变化的哈密顿量给出了相同的结果的情况下的拉格朗日。
英文摘要：
We apply the stochastic variational method to the action of the ideal fluid and showed that the Navier-Stokes equation is derived. In this variational method, the effect of dissipation is realized as the direct consequence of the fluctuation dissipation theorem. Differently from the previous works \cite{kk1,kk2}, we parameterize the Lagrangian of SVM in more general form. The form of the obtained equation is not modified but the definition of the transport coefficients are changed. We further discuss the formulation of SVM using the Hamiltonian and show that the variation of the Hamiltonian gives the same result as the case of the Lagrangian.
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