Symmetry in stationary and uniformly rotating solutions of active scalar equations

Einstein’s Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid

We reduce Einstein’s field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density μ and four dependent variables.Four of these equations do not depend on p and μ and the other two determine p and μ. PACS number(s): 04.20.Jb, 04.20.-q

L-approach of weak solutions to Stationary Rotating Oseen Equations in exterior domains

We establish the existence and uniqueness of weak solution of the three-dimensional nonhomogeneous stationary Oseen flow around a rotating body in an exterior domain. This article is extension of the previous results on the whole space. For the present extension to the case of exterior domains, we will use the localization procedure (see e.g. KoSo). In this way we combine the previous results (...

Stationary Axisymmetric Solutions of the Einstein Equations with Rigidly Rotating Perfect Fluid and Nonlinear Charged Sources

A class of stationary rigidly rotating perfect fluid coupled with nonlinear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state 3p + = constant. We use a structural function for the Born-Infeld non-linear electrodynamics which is invariant under duality rotations and a metric possessing...

Symmetry results for viscosity solutions of fully nonlinear uniformly elliptic equations

Stationary and Periodic Solutions of Differential Equations

A stochastic process ξ(t) = ξ(t,ω) (−∞ < t < ∞) with values in R is said to be stationary (in the strict sense) if for every finite sequence of numbers t1, . . . , tn the joint distribution of the random variables ξ(t1 + h), . . . , ξ(tn + h) is independent of h. If we replace the arbitrary number h by a multiple of a fixed number θ , h= kθ (k =±1,±2, . . . ), we get the definition of a periodi...