Lagrangian dynamics of the Navier-Stokes equation

Details Lagrangian dynamics of the Navier-Stokes equation Lagrangian dynamics of the Navier-Stokes equation

2005-08-15

arxiv.org/abs/physics/0508092v1

Proceeding of the ICAM 2005

Physics

Fluid Dynamics

9 pages, 1 figure, talk at the International Conference on Applied Mathematics 2005, Bandung

Scientific paper

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.

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