Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations
In this paper, we consider the Cauchy problem of the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities. When the shear and bulk viscosity coefficients are both given as a constant multiple of the mass density's power ($ \rho^\delta $ with $ \delta >...
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AIMS Press
2025-02-01
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| Series: | Communications in Analysis and Mechanics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2025007 |
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| author | Zhigang Wang |
| author_facet | Zhigang Wang |
| author_sort | Zhigang Wang |
| collection | DOAJ |
| description | In this paper, we consider the Cauchy problem of the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities. When the shear and bulk viscosity coefficients are both given as a constant multiple of the mass density's power ($ \rho^\delta $ with $ \delta > 1 $), we show that the $ L^{\infty} $ norms of $ \nabla u $, $ \nabla\rho^{\frac{\gamma-1}{2}} $ and $ \nabla\rho^{\frac{\delta-1}{2}} $ control the possible breakdown of classical solutions with far-field vacuum; this criterion is analogous to Serrin's blowup criterion for the compressible Navier–Stokes equations. |
| format | Article |
| id | doaj-art-03e2237de0df4eb880bbadd4fd737f5b |
| institution | OA Journals |
| issn | 2836-3310 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj-art-03e2237de0df4eb880bbadd4fd737f5b2025-08-20T01:54:34ZengAIMS PressCommunications in Analysis and Mechanics2836-33102025-02-0117114515810.3934/cam.2025007Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equationsZhigang Wang0School of Mathematics and Statistics, Fuyang Normal University, Anhui 236037, P.R.ChinaIn this paper, we consider the Cauchy problem of the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities. When the shear and bulk viscosity coefficients are both given as a constant multiple of the mass density's power ($ \rho^\delta $ with $ \delta > 1 $), we show that the $ L^{\infty} $ norms of $ \nabla u $, $ \nabla\rho^{\frac{\gamma-1}{2}} $ and $ \nabla\rho^{\frac{\delta-1}{2}} $ control the possible breakdown of classical solutions with far-field vacuum; this criterion is analogous to Serrin's blowup criterion for the compressible Navier–Stokes equations.https://www.aimspress.com/article/doi/10.3934/cam.2025007compressible navier–stokes equationsdegenerate viscosityfar-field vacuumclassical solutionsserrin-type blowup criterion |
| spellingShingle | Zhigang Wang Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations Communications in Analysis and Mechanics compressible navier–stokes equations degenerate viscosity far-field vacuum classical solutions serrin-type blowup criterion |
| title | Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations |
| title_full | Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations |
| title_fullStr | Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations |
| title_full_unstemmed | Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations |
| title_short | Serrin-type blowup Criterion for the degenerate compressible Navier-Stokes equations |
| title_sort | serrin type blowup criterion for the degenerate compressible navier stokes equations |
| topic | compressible navier–stokes equations degenerate viscosity far-field vacuum classical solutions serrin-type blowup criterion |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2025007 |
| work_keys_str_mv | AT zhigangwang serrintypeblowupcriterionforthedegeneratecompressiblenavierstokesequations |