On the solution operators arising from the gas-liquid two-phase problem in unbounded domains with finite depth
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916834172731392 |
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| author | Tu, Miao Zhang, Xin |
| author_facet | Tu, Miao Zhang, Xin |
| contents | This paper studies some evolution equations arising from the sharp interface problem of the compressible-incompressible Navier-Stokes equations in unbounded domains in $\mathbb{R}^N (N\geq2)$, where the viscous gases initially occupy the upper half space and the viscous liquids below initially lie in the strip-like domain. In order to establish the maximal $L_p$-$L_q$ regularity estimates of the evolution problem, we construct the R-solver of the resolvent problem associated to the gas-liquid two-phase operator. The crucial part of our proof lies in the analysis of the explicit resolvent operators defined in the unbounded domains with flat boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the solution operators arising from the gas-liquid two-phase problem in unbounded domains with finite depth Tu, Miao Zhang, Xin Analysis of PDEs 35Q30, 35R35 This paper studies some evolution equations arising from the sharp interface problem of the compressible-incompressible Navier-Stokes equations in unbounded domains in $\mathbb{R}^N (N\geq2)$, where the viscous gases initially occupy the upper half space and the viscous liquids below initially lie in the strip-like domain. In order to establish the maximal $L_p$-$L_q$ regularity estimates of the evolution problem, we construct the R-solver of the resolvent problem associated to the gas-liquid two-phase operator. The crucial part of our proof lies in the analysis of the explicit resolvent operators defined in the unbounded domains with flat boundaries. |
| title | On the solution operators arising from the gas-liquid two-phase problem in unbounded domains with finite depth |
| topic | Analysis of PDEs 35Q30, 35R35 |
| url | https://arxiv.org/abs/2507.06498 |