Application of Lie Groups to Fluid Kinematics

Introduction

We consider the fluid as existing within a domain referred to cartesian axes $x, y, z$.

There are two methods of describing fluid kinematic behavior: the Eulerian school and the Lagrangian school.

The Lagrangians examine the fluid from the point of view of individual particles moving through space. (Math often allows us to think about things even if they’re computationally infeasible.)

We take the dyadic derivative of velocity