This paper addresses the construction and stability of self-similar solutions to isentropic compressible Euler equations. These model a gas that implodes isotropically, ending in singularity formation finite time. The existence smooth vanish at infinity do not have vacuum regions was recently proved and, this paper, we provide first such profiles, characterization their spectrum radial perturba...

Ambipolar diffusion is a process occurring in partially ionised astrophysical systems that imparts complicated mathematical and physical nature to Ohm's law. The numerical codes solve the magnetohydrodynamic (MHD) equations have be able deal with singularities are naturally created system by ambipolar term. global aim calculate set of theoretical self-similar solutions nonlinear equation cylind...