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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| Format: | Article |
| Language: | English |
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AIMS Press
2025-02-01
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| Series: | Communications in Analysis and Mechanics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2025007 |
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| Summary: | 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. |
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| ISSN: | 2836-3310 |