Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy

Details Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy

2008-11-26

arxiv.org/abs/0811.4359v1

Proceedings of Symposia in Applied Mathematics 2009. Hyperbolic Problems: Theory, Numerics and Applications. Edited by: Eitan

Mathematics

Analysis of PDEs

7 pages, submitted

Scientific paper

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.

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