Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations
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| Format: | Preprint |
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2024
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| _version_ | 1866914726062063616 |
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| author | Peng, Yi Shi, Xiaoding Wu, Yuhang |
| author_facet | Peng, Yi Shi, Xiaoding Wu, Yuhang |
| contents | In this paper, the large time behavior of the solutions for the Cauchy problem to the one-dimensional compressible Navier-Stokes system with the motion of a viscous heat-conducting perfect polytropic gas is investigated.Our result shows that the combination of a viscous contact wave with rarefaction waves is asymptotically stable, when the large initial disturbance of the density, velocity and temperature belong to $H^{1}(\mathbb{R})$, $L^{2}(\mathbb{R})\cap L^{4}(\mathbb{R})$ and $L^{2}(\mathbb{R})$, provided the strength of the combination waves is suitably small. In addition, the initial disturbance on the derivation of velocity and temperature belong to $L^{2}(\mathbb{R})$ can be arbitrarily large. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_15663 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations Peng, Yi Shi, Xiaoding Wu, Yuhang Analysis of PDEs 35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30 G.1.8 In this paper, the large time behavior of the solutions for the Cauchy problem to the one-dimensional compressible Navier-Stokes system with the motion of a viscous heat-conducting perfect polytropic gas is investigated.Our result shows that the combination of a viscous contact wave with rarefaction waves is asymptotically stable, when the large initial disturbance of the density, velocity and temperature belong to $H^{1}(\mathbb{R})$, $L^{2}(\mathbb{R})\cap L^{4}(\mathbb{R})$ and $L^{2}(\mathbb{R})$, provided the strength of the combination waves is suitably small. In addition, the initial disturbance on the derivation of velocity and temperature belong to $L^{2}(\mathbb{R})$ can be arbitrarily large. |
| title | Nonlinear Stability for the Superposition of Viscous Contact Wave and Rarefaction Waves to Non-isentropic Compressible Navier-Stokes System with General Initial Perturbations |
| topic | Analysis of PDEs 35Q35, 35B65, 76N10, 35M10, 35B40, 35C20, 76T30 G.1.8 |
| url | https://arxiv.org/abs/2403.15663 |