Lagrangian dynamics of the Navier-Stokes equation
A. Sulaiman, L. T. Handoko
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 μ with appropriate content describing the fluid dynamics, i.e. μ= (Φ, -). An example of applying the lagrangian to the interaction of fluid in a solitonic medium is also given.
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