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On the blow up criterion for the 2-D compressible Navier-Stokes equations

Lingyu Jiang, Yidong Wang (2010)

Czechoslovak Mathematical Journal

Motivated by [10], we prove that the upper bound of the density function ρ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.

On the Cauchy problem for the equations of ideal compressible MHD fluids with radiation

Christian Rohde, Wojciech M. Zajączkowski (2003)

Applications of Mathematics

We consider a system of balance laws describing the motion of an ionized compressible fluid interacting with magnetic fields and radiation effects. The local-in-time existence of a unique smooth solution for the Cauchy problem is proven. The proof follows from the method of successive approximations.

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