Nishida-Smoller type large solutions for the compressible Navier-Stokes equations with slip boundary conditions in 3D exterior domains
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912305479942144 |
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| author | Xie, Minghong Xu, Saiguo Zhang, Yinghui |
| author_facet | Xie, Minghong Xu, Saiguo Zhang, Yinghui |
| contents | This paper investigates the global existence of classical solutions to the isentropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. It is shown that the classical solutions with large initial energy and vacuum exist globally in time when the adiabatic exponent $γ>1$ is sufficiently close to 1 (near-isothermal regime). This constitutes an extension of the celebrated result for the one-dimensional Cauchy problem of the isentropic Euler equations that has been established in 1973 by Nishida and Smoller (Comm. Pure Appl. Math. 26 (1973), 183-200). To the best of our knowledge, we establish the first result on the global existence of large-energy solutions with vacuum to the compressible Navier-Stokes equations with slip boundary condition in a 3D exterior domain, which improves previous related works where either small initial energy is required or boundary effects are ignored. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nishida-Smoller type large solutions for the compressible Navier-Stokes equations with slip boundary conditions in 3D exterior domains Xie, Minghong Xu, Saiguo Zhang, Yinghui Analysis of PDEs This paper investigates the global existence of classical solutions to the isentropic compressible Navier-Stokes equations with slip boundary condition in a three-dimensional (3D) exterior domain. It is shown that the classical solutions with large initial energy and vacuum exist globally in time when the adiabatic exponent $γ>1$ is sufficiently close to 1 (near-isothermal regime). This constitutes an extension of the celebrated result for the one-dimensional Cauchy problem of the isentropic Euler equations that has been established in 1973 by Nishida and Smoller (Comm. Pure Appl. Math. 26 (1973), 183-200). To the best of our knowledge, we establish the first result on the global existence of large-energy solutions with vacuum to the compressible Navier-Stokes equations with slip boundary condition in a 3D exterior domain, which improves previous related works where either small initial energy is required or boundary effects are ignored. |
| title | Nishida-Smoller type large solutions for the compressible Navier-Stokes equations with slip boundary conditions in 3D exterior domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.01288 |