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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2407.07001 |
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| _version_ | 1866916317775265792 |
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| author | Kang, Kyungkeun Lai, Baishun Lai, Chen-Chih Tsai, Tai-Peng |
| author_facet | Kang, Kyungkeun Lai, Baishun Lai, Chen-Chih Tsai, Tai-Peng |
| contents | In this paper, we present a series of applications of the pointwise estimates of the (unrestricted) Green tensor of the nonstationary Stokes system in the half space, established in our previous work [CMP 2023]. First, we show the $L^1$-$L^q$ estimates for the Stokes flow with possibly non-solenoidal $L^1$ initial data, generalizing the results of Giga-Matsui-Shimizu [Math. Z. 1999] and Desch-Hieber-Prüss [J. Evol. Equ. 2001]. Second, we construct mild solutions of the Navier-Stokes equations in the half space with mixed-type pointwise decay or with pointwise decay alongside boundary vanishing. Finally, we explore various coupled fluid systems in the half space including viscous resistive magnetohydrodynamics equations, a coupled system for the flow and the magnetic field of MHD type, and the nematic liquid crystal flow. For each of these systems, we construct mild solutions in $L^q$, pointwise decay, and uniformly local $L^q$ spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07001 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Applications of the Green tensor estimates of the nonstationary Stokes system in the half space Kang, Kyungkeun Lai, Baishun Lai, Chen-Chih Tsai, Tai-Peng Analysis of PDEs Mathematical Physics In this paper, we present a series of applications of the pointwise estimates of the (unrestricted) Green tensor of the nonstationary Stokes system in the half space, established in our previous work [CMP 2023]. First, we show the $L^1$-$L^q$ estimates for the Stokes flow with possibly non-solenoidal $L^1$ initial data, generalizing the results of Giga-Matsui-Shimizu [Math. Z. 1999] and Desch-Hieber-Prüss [J. Evol. Equ. 2001]. Second, we construct mild solutions of the Navier-Stokes equations in the half space with mixed-type pointwise decay or with pointwise decay alongside boundary vanishing. Finally, we explore various coupled fluid systems in the half space including viscous resistive magnetohydrodynamics equations, a coupled system for the flow and the magnetic field of MHD type, and the nematic liquid crystal flow. For each of these systems, we construct mild solutions in $L^q$, pointwise decay, and uniformly local $L^q$ spaces. |
| title | Applications of the Green tensor estimates of the nonstationary Stokes system in the half space |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2407.07001 |