Applications of Fluid Dynamics Based on Gauge Field Theory Approach

Abstract

Recently, a new approach to deal with the Navier-Stokes equation has been developed. The equation which governs the uid dynamics is a a non-linear one and then generally unsolvable. In the new approach, the uid dynamics is described using the relativistic gauge invariant bosonic lagrangian which could reproduce the Navier-Stokes equation as its equation of motion through the Euler-Lagrange principle. Based on the lagrangian we model the uid dynamics phenomenon as scattering of either three or four uid bunches represented by the gauge eld A = ( ; ~A) ..d 2 j~vj2 .. V;..d~v with ~v is velocity and d is a parameter to adjust the dimension for any potential V . Further we present all relevant Fynman rules and diagrams, and also provide complete calculations for all vertices induced by three and four uid elds interactions.