Sharp lifespan estimate for the compressible Euler system with critical time-dependent damping in $\R^2$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916130060238848 |
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| author | Cai, Lv Lai, Ning-An Su, Wen-Ze |
| author_facet | Cai, Lv Lai, Ning-An Su, Wen-Ze |
| contents | This paper concerns the long time existence to the smooth solutions of the compressible Euler system with critical time dependent damping in $\R^2$. We establish the sharp lifespan estimate from below, with respect to the small parameter of the initial perturbation. For this end, the vector fields $\widehat{Z}$ (defined below) are used instead of the usual one $Z$, to get better decay for the linear error terms. This idea may also apply to the long time behavior study of nonlinear wave equations with time-dependent damping. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11516 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp lifespan estimate for the compressible Euler system with critical time-dependent damping in $\R^2$ Cai, Lv Lai, Ning-An Su, Wen-Ze Analysis of PDEs This paper concerns the long time existence to the smooth solutions of the compressible Euler system with critical time dependent damping in $\R^2$. We establish the sharp lifespan estimate from below, with respect to the small parameter of the initial perturbation. For this end, the vector fields $\widehat{Z}$ (defined below) are used instead of the usual one $Z$, to get better decay for the linear error terms. This idea may also apply to the long time behavior study of nonlinear wave equations with time-dependent damping. |
| title | Sharp lifespan estimate for the compressible Euler system with critical time-dependent damping in $\R^2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.11516 |