Abstract
We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for a dynamic fluid, to magneto-hydrodynamic equations and to the Poisson-Boltzmann equation.
Highlights
Fluid dynamics is one of the most well understood subjects in classical physics [1] and yet continues to be an actively developing field of research even today
We propose in this paper the modeling of fluid dynamics as moving surfaces in an electromagnetic field and show that this concept non-trivially generalizes classical fluid dynamics
In this subsection we demonstrate that, the equations of motion simplify to Maxwell equations for stationary interfaces C = 0 and massless ρ = 0 three manifolds embedded in Minkowski space
Summary
Fluid dynamics is one of the most well understood subjects in classical physics [1] and yet continues to be an actively developing field of research even today. We propose in this paper the modeling of fluid dynamics as moving surfaces in an electromagnetic field and show that this concept non-trivially generalizes classical fluid dynamics. We deduce general partial differential equations for moving manifolds in an electromagnetic field and demonstrate that the equations, in different conditions, simplify to the Euler equation for fluid dynamics, the Poisson-Boltzmann equation for describing the electric potential distribution on surface and the Maxwell equations for electrodynamics. The problem formulates as: find equations of motion in electromagnetic field for a closed, continuously differentiated and smooth two dimensional manifold in Euclidean space (non-relativistic case) or three manifolds in Minkowski spacetime (relativistic case). Definition of the Lagrangian [22] by subtracting potential energy from the kinetic energy and the minimum action principal yields nonlinear equations for moving surfaces in electromagnetic field
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