Global stability for compressible isentropic Navier-Stokes equations in 3D bounded domains with Navier-slip boundary conditions
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| Format: | Preprint |
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2025
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| _version_ | 1866917019230666752 |
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| author | Liu, Yang Wu, Guochun Zhong, Xin |
| author_facet | Liu, Yang Wu, Guochun Zhong, Xin |
| contents | We investigate the global stability of large solutions to the compressible isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the strong solutions converge to an equilibrium state exponentially in the $L^2$-norm provided the density is essentially uniform-in-time bounded from above. Moreover, we obtain that the density converges to its equilibrium state exponentially in the $L^\infty$-norm if additionally the initial density is bounded away from zero. Furthermore, we derive that the vacuum states will not vanish for any time provided vacuum appears (even at a point) initially. This is the first result concerning the global stability for large strong solutions of compressible Navier-Stokes equations with vacuum in 3D general bounded domains. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global stability for compressible isentropic Navier-Stokes equations in 3D bounded domains with Navier-slip boundary conditions Liu, Yang Wu, Guochun Zhong, Xin Analysis of PDEs We investigate the global stability of large solutions to the compressible isentropic Navier-Stokes equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the strong solutions converge to an equilibrium state exponentially in the $L^2$-norm provided the density is essentially uniform-in-time bounded from above. Moreover, we obtain that the density converges to its equilibrium state exponentially in the $L^\infty$-norm if additionally the initial density is bounded away from zero. Furthermore, we derive that the vacuum states will not vanish for any time provided vacuum appears (even at a point) initially. This is the first result concerning the global stability for large strong solutions of compressible Navier-Stokes equations with vacuum in 3D general bounded domains. |
| title | Global stability for compressible isentropic Navier-Stokes equations in 3D bounded domains with Navier-slip boundary conditions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.17136 |