Title: Knotted solutions, from electromagnetism to fluid dynamics,
Abstract: Knotted solutions to electromagnetism and fluid dynamics are investigated,
based on relations we find between the two subjects. We can write fluid
dynamics in electromagnetism language, but only on an initial surface, or for
linear perturbations, and we use this map to find knotted fluid solutions, as
well as new electromagnetic solutions. We find that knotted solutions of
Maxwell electromagnetism are also solutions of more general nonlinear theories,
like Born-Infeld, and including ones which contain quantum corrections from
couplings with other modes, like Euler-Heisenberg and string theory DBI. Null
configurations in electromagnetism can be described as a null pressureless
fluid, and from this map we can find null fluid knotted solutions. A type of
nonrelativistic reduction of the relativistic fluid equations is described,
which allows us to find also solutions of the (nonrelativistic) Euler's
equations.