Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911826762006528 |
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| author | Chen, Wenhui Ikehata, Ryo |
| author_facet | Chen, Wenhui Ikehata, Ryo |
| contents | In this paper, we consider the linearized compressible Navier-Stokes equations in the whole space $\mathbb{R}^n$. Concerning initial datum with suitable regularities, we introduce a new threshold $|\mathbb{B}_0|=0$ to distinguish different large-time behaviors. Particularly in the lower-dimensions, optimal growth estimates ($n=1$ polynomial growth, $n=2$ logarithmic growth) hold when $|\mathbb{B}_0|>0$, whereas optimal decay estimates hold when $|\mathbb{B}_0|=0$. Furthermore, we derive asymptotic profiles of solutions with weighted $L^1$ datum as large-time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00836 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations Chen, Wenhui Ikehata, Ryo Analysis of PDEs In this paper, we consider the linearized compressible Navier-Stokes equations in the whole space $\mathbb{R}^n$. Concerning initial datum with suitable regularities, we introduce a new threshold $|\mathbb{B}_0|=0$ to distinguish different large-time behaviors. Particularly in the lower-dimensions, optimal growth estimates ($n=1$ polynomial growth, $n=2$ logarithmic growth) hold when $|\mathbb{B}_0|>0$, whereas optimal decay estimates hold when $|\mathbb{B}_0|=0$. Furthermore, we derive asymptotic profiles of solutions with weighted $L^1$ datum as large-time. |
| title | Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2211.00836 |