Blow up criteria for the compressible Navier–Stokes equations

Research output: Chapter in Book/Report/Conference proceedingChapter

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 Jan 1

Publication series

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

Fingerprint

Blow-up Criterion
Compressible Navier-Stokes Equations
Strong Solution
Integrability
3D
Boundedness
Divergence
Viscosity
Heat
Regularity
Restriction
Norm
Partial
Imply
Gas

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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. https://doi.org/10.1090/conm/710/14364
Choe, Hi Jun ; Yang, Minsuk. / Blow up criteria for the compressible Navier–Stokes equations. Contemporary Mathematics. American Mathematical Society, 2018. pp. 65-84 (Contemporary Mathematics).
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Choe, HJ & Yang, M 2018, Blow up criteria for the compressible Navier–Stokes equations. in Contemporary Mathematics. Contemporary Mathematics, vol. 710, American Mathematical Society, pp. 65-84. https://doi.org/10.1090/conm/710/14364

Blow up criteria for the compressible Navier–Stokes equations. / Choe, Hi Jun; Yang, Minsuk.

Contemporary Mathematics. American Mathematical Society, 2018. p. 65-84 (Contemporary Mathematics; Vol. 710).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Choe HJ, Yang M. Blow up criteria for the compressible Navier–Stokes equations. In Contemporary Mathematics. American Mathematical Society. 2018. p. 65-84. (Contemporary Mathematics). https://doi.org/10.1090/conm/710/14364