Long-time behavior toward composite wave of shocks for 3D barotropic navier-stokes system
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911920166010880 |
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| author | Kang, Moon-Jin Lee, Hobin |
| author_facet | Kang, Moon-Jin Lee, Hobin |
| contents | We consider the barotropic Navier-Stokes system in three space dimensions with periodic boundary condition in the transversal direction. We show the long-time behavior of the 3D barotropic Navier-Stokes flow perturbed from a composition of two shock waves with suitably small amplitudes. We prove that the perturbed Navier-Stokes flow converges, uniformly in space, towards a composition of two planar viscous shock waves as time goes to infinity, up to dynamical shifts. This is the first result on time-asymptotic stability of composite wave of two shocks for multi-D Navier-Stokes system. The main part of proof is based on the method of a-contraction with shifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_11215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long-time behavior toward composite wave of shocks for 3D barotropic navier-stokes system Kang, Moon-Jin Lee, Hobin Analysis of PDEs We consider the barotropic Navier-Stokes system in three space dimensions with periodic boundary condition in the transversal direction. We show the long-time behavior of the 3D barotropic Navier-Stokes flow perturbed from a composition of two shock waves with suitably small amplitudes. We prove that the perturbed Navier-Stokes flow converges, uniformly in space, towards a composition of two planar viscous shock waves as time goes to infinity, up to dynamical shifts. This is the first result on time-asymptotic stability of composite wave of two shocks for multi-D Navier-Stokes system. The main part of proof is based on the method of a-contraction with shifts. |
| title | Long-time behavior toward composite wave of shocks for 3D barotropic navier-stokes system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.11215 |