Stability of Riemann Shocks for isothermal Euler by Inviscid limits of global-in-time large Navier-Stokes flows
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916748218859520 |
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| author | Eo, Saehoon Eun, Namhyun Kang, Moon-Jin Oh, HyeonSeop |
| author_facet | Eo, Saehoon Eun, Namhyun Kang, Moon-Jin Oh, HyeonSeop |
| contents | In this paper, we study the isothermal gas dynamics. We first establish the global existence of strong solutions to the one-dimensional isothermal Navier-Stokes system for smooth initial data without any smallness conditions, assuming that the initial density has strictly positive lower bound. The existence result allows for possibly degenerate viscosity coefficients and admits different asymptotic states at the far fields. We then prove a contraction property for the strong solutions perturbed from viscous shocks, yielding uniform estimates with respect to the viscosity coefficients. This covers any large perturbations, and consequently, we establish the inviscid limits and their stability estimate. In other words, we demonstrate the stability of Riemann shocks to the one-dimensional isothermal Euler system in the class of vanishing viscosity limits of the associated Navier-Stokes system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Riemann Shocks for isothermal Euler by Inviscid limits of global-in-time large Navier-Stokes flows Eo, Saehoon Eun, Namhyun Kang, Moon-Jin Oh, HyeonSeop Analysis of PDEs Mathematical Physics 35Q30, 76N10, 35B35 In this paper, we study the isothermal gas dynamics. We first establish the global existence of strong solutions to the one-dimensional isothermal Navier-Stokes system for smooth initial data without any smallness conditions, assuming that the initial density has strictly positive lower bound. The existence result allows for possibly degenerate viscosity coefficients and admits different asymptotic states at the far fields. We then prove a contraction property for the strong solutions perturbed from viscous shocks, yielding uniform estimates with respect to the viscosity coefficients. This covers any large perturbations, and consequently, we establish the inviscid limits and their stability estimate. In other words, we demonstrate the stability of Riemann shocks to the one-dimensional isothermal Euler system in the class of vanishing viscosity limits of the associated Navier-Stokes system. |
| title | Stability of Riemann Shocks for isothermal Euler by Inviscid limits of global-in-time large Navier-Stokes flows |
| topic | Analysis of PDEs Mathematical Physics 35Q30, 76N10, 35B35 |
| url | https://arxiv.org/abs/2505.15078 |