Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929705539600384 |
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| author | Shao, Feng Wei, Dongyi Wang, Shumao Zhang, Zhifei |
| author_facet | Shao, Feng Wei, Dongyi Wang, Shumao Zhang, Zhifei |
| contents | In this paper, we prove the blow-up of the $3$-D isentropic compressible Navier-Stokes equations for the adiabatic exponent $γ=5/3$, which corresponds to the law of monatomic gases. This is the degenerate case in the sense of [Merle, Raphaël, Rodnianski and Szeftel, Ann. of Math. (2), 196 (2022), 567-778; Ann. of Math. (2), 196 (2022), 779-889]. Motivated by these breakthrough works, we first establish the existence of a sequence of smooth, self-similar imploding solutions to the compressible Euler equations for $γ=5/3$. Subsequently, we utilize these self-similar profiles to construct smooth, asymptotically self-similar blow-up solutions to the compressible Navier-Stokes equations for monatomic gases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases Shao, Feng Wei, Dongyi Wang, Shumao Zhang, Zhifei Analysis of PDEs In this paper, we prove the blow-up of the $3$-D isentropic compressible Navier-Stokes equations for the adiabatic exponent $γ=5/3$, which corresponds to the law of monatomic gases. This is the degenerate case in the sense of [Merle, Raphaël, Rodnianski and Szeftel, Ann. of Math. (2), 196 (2022), 567-778; Ann. of Math. (2), 196 (2022), 779-889]. Motivated by these breakthrough works, we first establish the existence of a sequence of smooth, self-similar imploding solutions to the compressible Euler equations for $γ=5/3$. Subsequently, we utilize these self-similar profiles to construct smooth, asymptotically self-similar blow-up solutions to the compressible Navier-Stokes equations for monatomic gases. |
| title | Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.15701 |