相对论性流体的拉格朗日密度与运动方程及连续方程

Agrange density,motion equation and continuous equation of relativistic fluid

本文从相对论性理想流体的能量动量张量出发,在合理的假设之下给出了相对论性流体的拉格朗日密度函数,并以此为基础在最小作用量原理下导出了相对论性流体的运动方程.在低速低压下,本文所得的运动方程可退化为纳维-斯托克斯方程.本文还讨论了流体的连续方程,本文发现,即使是在平直时空的低速下,牛顿力学下流体的连续方程也只有在压强及外力的影响可以忽略时才能成立.

Under reasonable assumptions,this paper presents a Lagrangian density of relativistic fluid from the energy-momentum tensor of the relativistic fluid,and presents the equation of motion for relativistic fluid based on the Lagrangian density and the principle of least action.In the limit of low speed and low pressure our equations of motion reduces to Navier-Stokes equations.The continuity equation of fluid is also discussed.It is found that the continuity equation of fluid in Newtonian mechanics can be established only when the influence of pressure and external force can be neglected,even at the low speed of flat space-time.