Novel self-similar rotating solutions of nonideal transverse magnetohydrodynamics

Nonexistence of self-similar singularities in the ideal magnetohydrodynamics

In this paper we exclude the scenario of apparition of finite time singularity in the form of self-similar singularities in the ideal magnetohydrodynamic equations, assuming suitable integrability conditions on the vorticity and the magnetic field. We also consider more sophisticated possibility of asymptotically self-similar singularities, which means that the local classical solution converge...

Self-similar condensation of rotating magnetized self-gravitating isothermal filaments

Ordinary differential equations describing the self-similar collapse of a rotating, magnetized, selfgravitating and isothermal filament are derived. Explicit homologous solutions are studied with special emphasis on the bifurcation that occurs at the magnetosonic critical point. It is shown that there is a critical value for the toroidal magnetic field slope at the origin above which no bifurca...

New Self - Similar Solutions of theNonlinear

Continuous Self-Similar Evaporation of a Rotating Cosmic String Loop

A solution of the linearized Einstein and Nambu-Goto equations is constructed which describes the evaporation of a certain type of rotating cosmic string – the Allen-Casper-Ottewill loop – under the action of its own self-gravity. The solution evaporates self-similarly, and radiates away all its mass-energy and momentum in a finite time. Furthermore, the corresponding weak-field metric can be m...

Remarks on rotating shallow-water magnetohydrodynamics

We show how the rotating shallow-water MHD model, which was proposed in the solar tachocline context, may be systematically derived by vertical averaging of the full MHD equations for the rotating magneto fluid under the influence of gravity. The procedure highlights the main approximations and the domain of validity of the model, and allows for multi-layer generalizations and, hence, inclusion...