Blow up criteria for the compressible Navier–Stokes equations

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Abstract

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
Pages65-84
Number of pages20
DOIs
Publication statusPublished - 2018

Publication series

NameContemporary Mathematics
Volume710
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Bibliographical note

Funding Information:
H. Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2015R1A5A1009350). M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2016R1C1B2015731).

Publisher Copyright:
© 2018 American Mathematical Society.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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