Global weak solutions and incompressible limit to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and large initial data
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909870516600832 |
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| author | Wang, Shuai Wu, Guochun Zhong, Xin |
| author_facet | Wang, Shuai Wu, Guochun Zhong, Xin |
| contents | We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large. Moreover, we show that such solutions converge globally in time to a weak solution of the inhomogeneous incompressible Navier-Stokes equations as the bulk viscosity coefficient tends to infinity. In particular, the large initial data and an initial patch of density as well as a vacuum are allowed. Our method relies on a Desjardins-type logarithmic interpolation inequality and some new techniques based on the effective viscous flux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03505 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global weak solutions and incompressible limit to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and large initial data Wang, Shuai Wu, Guochun Zhong, Xin Analysis of PDEs We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large. Moreover, we show that such solutions converge globally in time to a weak solution of the inhomogeneous incompressible Navier-Stokes equations as the bulk viscosity coefficient tends to infinity. In particular, the large initial data and an initial patch of density as well as a vacuum are allowed. Our method relies on a Desjardins-type logarithmic interpolation inequality and some new techniques based on the effective viscous flux. |
| title | Global weak solutions and incompressible limit to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and large initial data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.03505 |