Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914627940515840 |
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| author | Iwabuchi, Tsukasa hAodha, Dáithí Ó |
| author_facet | Iwabuchi, Tsukasa hAodha, Dáithí Ó |
| contents | We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution. This allows us to obtain a bound from below for the time-decay of the solution in $L^\infty$, proving that our decay estimate in that space is sharp. The decay rate is the same as that of the linear problem for curl-free flow. We also obtain an estimate for a scalar system related to curl-free solutions to the compressible Navier-Stokes equations in a weighted Lebesgue space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04811 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations Iwabuchi, Tsukasa hAodha, Dáithí Ó Analysis of PDEs We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution. This allows us to obtain a bound from below for the time-decay of the solution in $L^\infty$, proving that our decay estimate in that space is sharp. The decay rate is the same as that of the linear problem for curl-free flow. We also obtain an estimate for a scalar system related to curl-free solutions to the compressible Navier-Stokes equations in a weighted Lebesgue space. |
| title | Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.04811 |