不可压粘性流体力学初值问题的拟变分原理及其广义变分原理

Quasi-variational principles of incompressible viscous fluids

利用Laplace变换将不可压粘性流体动力学的方程与边界条件变换到象空间上,同时也就把初值条件引入到象空间的方程内。然后在象空间利用变积方法建立不可压粘性流体动力学的拟变分原理和广义拟变分原理,再将它们拉氏反演到原空间内,即得时间域内的不可压粘性流体动力学的变分原理及其广义变分原理。最后用一个具体的例子对原理的应用进行了说明。

Using Laplace transform this paper maps the governing equations and boundary conditions of incompressible viscous fluids into image space,thus at the same time,introducing the initial condition to the equations in the image space.Next,in image space the quasi-variational principles for incompressible viscous fluid are established by utilizing the variational integral method.Then transform these principles into the original space（i.e.,the time domain） by Laplace inverse transform.Finally an example are presented for demonstration.