Global Classical Solutions to 3D Compressible Navier-Stokes System with Vacuum in Bounded Domains under Non-Slip Boundary Conditions
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866912070313705472 |
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| author | Fan, Xinyu Li, Jing |
| author_facet | Fan, Xinyu Li, Jing |
| contents | This paper studies the global well-posedness of classical solutions to the isentropic compressible Navier-Stokes equations in 3D domains D under non-slip boundary conditions. D will separate into the inner and boundary parts along a free surface: In the inner part, the density is allowed to vanish and the gradient of it grows with an exponential rate when vacuum appears initially; while in the boundary part, no vacuum forms and the higher order derivatives of the density remain uniformly bounded. We utilize the Lagrangian coordinates introduced by Christodoulou-Lindblad to study such dichotomy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_13708 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Global Classical Solutions to 3D Compressible Navier-Stokes System with Vacuum in Bounded Domains under Non-Slip Boundary Conditions Fan, Xinyu Li, Jing Analysis of PDEs This paper studies the global well-posedness of classical solutions to the isentropic compressible Navier-Stokes equations in 3D domains D under non-slip boundary conditions. D will separate into the inner and boundary parts along a free surface: In the inner part, the density is allowed to vanish and the gradient of it grows with an exponential rate when vacuum appears initially; while in the boundary part, no vacuum forms and the higher order derivatives of the density remain uniformly bounded. We utilize the Lagrangian coordinates introduced by Christodoulou-Lindblad to study such dichotomy. |
| title | Global Classical Solutions to 3D Compressible Navier-Stokes System with Vacuum in Bounded Domains under Non-Slip Boundary Conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2112.13708 |