Lagrangian dynamics of the Navier-Stokes equation

Abstract

Most researches on fluid dynamics are mostly dedicated to obtain the solutions of Navier-Stokes equation which governs fluid flow with particular boundary conditions and approximations. We propose an alternative approach to deal with fluid dynamics using the lagrangian. We attempt to develop a gauge invariant lagrangian which reconstructs the Navier-Stokes equation through the Euler-Lagrange equation. The lagrangian consists of gauge boson field $\A_\mu$ with appropriate content describing the fluid dynamics, i.e. $\A_\mu = (\Phi, -\uv)$. An example of applying the lagrangian to the interaction of fluid in a solitonic medium is also given.