%0 Journal Article
%T Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy
%A Olga Rozanova
%J Mathematics
%D 2008
%I arXiv
%X We prove that the smooth solutions to the Cauchy problem for the three-dimensional compressible barotropic magnetohydrodynamic equations with conserved total mass and finite total energy lose the initial smoothness within a finite time. Further, we show that the same result holds for the solution to the Cauchy problem for the multidimensional compressible Navier-Stokes system. Moreover, for the solution with a finite momentum of inertia we get the two-sided estimates of different components of total energy.
%U http://arxiv.org/abs/0811.4359v1