Lagrangian dynamics of the Navier-Stokes equation
arXiv:physics/0508092
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 $\A_μ$ with appropriate content describing the fluid dynamics, i.e. $\A_μ= (Φ, -\uv)$. An example of applying the lagrangian to the interaction of fluid in a solitonic medium is also given.
9 pages, 1 figure, talk at the International Conference on Applied Mathematics 2005, Bandung