Geodesic
On the blow up criterion for the 2-D compressible Navier-Stokes equations
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 195-209.

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Motivated by [10], we prove that the upper bound of the density function $\rho $ 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.
Classification : 35B44, 35Q30, 35Q35, 76D03
Keywords: compressible Navier-Stokes equations; classical solutions; blow up criterion 
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     title = {On the blow up criterion for the {2-D} compressible {Navier-Stokes} equations},
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Jiang, Lingyu; Wang, Yidong. On the blow up criterion for the 2-D compressible Navier-Stokes equations. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 195-209. http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a16/