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compressible Navier-Stokes equations; classical solutions; blow up criterion
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.
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[9] Xin, Z. P.: Blow up of smooth solutions to the compressible Navier-Stokes equation with compact density. Comm. Pure Appl. Math. 51 (1998), 229-240. DOI 10.1002/(SICI)1097-0312(199803)51:3<229::AID-CPA1>3.0.CO;2-C | MR 1488513
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