Blow up criteria for the compressible Navier–Stokes equations

Research output: Chapter in Book/Report/Conference proceedingChapter


We study the strong solution to the 3-D compressible Navier– Stokes equations. We propose a new blow up criterion for barotropic gases in terms of the integral norm of density ρ and the divergence of the velocity u without any restriction on the physical viscosity constants. Our blow up criteria can be seen as a partial realization of the underlying principle that higher integrability implies boundedness and then eventual regularity. We also present a similar blow-up criterion for heat conducting gases.

Original languageEnglish
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Number of pages20
Publication statusPublished - 2018 Jan 1

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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  • Cite this

    Choe, H. J., & Yang, M. (2018). Blow up criteria for the compressible Navier–Stokes equations. In Contemporary Mathematics (pp. 65-84). (Contemporary Mathematics; Vol. 710). American Mathematical Society.