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

Olga Rozanova

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arXiv · 0811.4359

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

Olga Rozanova

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Abstract

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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Olga Rozanova. 2008-11-26. Blow up of smooth solutions to the barotropic compressible magnetohydrodynamic equations with finite mass and energy. https://arxiv.org/abs/0811.4359

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