Local classical solutions to Navier-Stokes equations with degenerate viscosities and vacuum
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909327537733632 |
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| author | Li, Yachun Yu, Shaojun |
| author_facet | Li, Yachun Yu, Shaojun |
| contents | We consider the 3D isentropic compressible Navier-Stokes equations with degenerate viscousities and vacuum. The degenerate viscosities $μ(ρ)$ and $λ(ρ)$ are proportional to some power of density, while the powers of density in $μ(ρ)$ and $λ(ρ)$ are different(i.e., $δ_1\neq δ_2$). The local well-posedness of classical solution is established by introducing a ``quasi-symmetric hyperbolic''--``degenerate elliptic'' coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates. In particular, the initial data allows vacuum in an open set and we do not need any initial compatibility conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local classical solutions to Navier-Stokes equations with degenerate viscosities and vacuum Li, Yachun Yu, Shaojun Analysis of PDEs We consider the 3D isentropic compressible Navier-Stokes equations with degenerate viscousities and vacuum. The degenerate viscosities $μ(ρ)$ and $λ(ρ)$ are proportional to some power of density, while the powers of density in $μ(ρ)$ and $λ(ρ)$ are different(i.e., $δ_1\neq δ_2$). The local well-posedness of classical solution is established by introducing a ``quasi-symmetric hyperbolic''--``degenerate elliptic'' coupled structure to control the behavior of the velocity of the fluid near the vacuum and give some uniform estimates. In particular, the initial data allows vacuum in an open set and we do not need any initial compatibility conditions. |
| title | Local classical solutions to Navier-Stokes equations with degenerate viscosities and vacuum |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.18137 |