Blow up criteria for the compressible Navier–Stokes equations

Hi Jun Choe; Minsuk Yang

doi:10.1090/conm/710/14364

Blow up criteria for the compressible Navier–Stokes equations

Hi Jun Choe, Minsuk Yang

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Citation (Scopus)

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 language	English
Title of host publication	Contemporary Mathematics
Publisher	American Mathematical Society
Pages	65-84
Number of pages	20
DOIs	https://doi.org/10.1090/conm/710/14364
Publication status	Published - 2018

Publication series

Name	Contemporary Mathematics
Volume	710
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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10.1090/conm/710/14364

Cite this

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title = "Blow up criteria for the compressible Navier–Stokes equations",

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.",

author = "Choe, {Hi Jun} and Minsuk Yang",

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: {\textcopyright} 2018 American Mathematical Society.",

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doi = "10.1090/conm/710/14364",

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AU - Yang, Minsuk

N1 - 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.

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N2 - 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.

AB - 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.

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BT - Contemporary Mathematics

PB - American Mathematical Society

ER -

Blow up criteria for the compressible Navier–Stokes equations

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