Nonexistence results for compressible non-Newtonian fluid with magnetic effects in the whole space

Details Nonexistence results for compressible non-Newtonian fluid with magnetic effects in the whole space Nonexistence results for compressible non-Newtonian fluid with magnetic effects in the whole space

2010-08-26

arxiv.org/abs/1008.4455v1

Journal of Mathematical Analysis and Applications 371 (2010), pp. 190-194

Mathematics

Analysis of PDEs

8 pages

Scientific paper

We consider a generalization of the compressible barotropic Navier-Stokes equations to the case of non-Newtonian fluid in the whole space. The viscosity tensor is assumed to be coercive with an exponent $q>1.$ We prove that if the total mass and momentum of the system are conserved, then one can find a constant $q_0>1$ depending on the dimension of space $n$ and the heat ratio $\gamma$ such that for $q\in [q_0,n)$ there exists no global in time smooth solution to the Cauchy problem. We prove also an analogous result for solutions to equations of magnetohydrodynamic non-Newtonian fluid in 3D space.

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