$\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913498863239168 |
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| author | Maryani, Sri Murata, Miho |
| author_facet | Maryani, Sri Murata, Miho |
| contents | In this paper, we consider a resolvent problem arising from the free boundary value problem for the compressible fluid model of Korteweg type, which is called as the Navier-Stokes-Korteweg system, with surface tension in the half-space. The Navier-Stokes-Korteweg system is known as a diffuse interface model for liquid-vapor two-phase flows. Our purpose is to show the $\mathcal R$-boundedness for the solution operator families of the resolvent problem, which gives us the maximal regularity estimates in the $L_p$-in-time and $L_q$-in-space setting by applying the Weis's operator valued Fourier multiplier theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space Maryani, Sri Murata, Miho Analysis of PDEs 35Q35, 76N10 In this paper, we consider a resolvent problem arising from the free boundary value problem for the compressible fluid model of Korteweg type, which is called as the Navier-Stokes-Korteweg system, with surface tension in the half-space. The Navier-Stokes-Korteweg system is known as a diffuse interface model for liquid-vapor two-phase flows. Our purpose is to show the $\mathcal R$-boundedness for the solution operator families of the resolvent problem, which gives us the maximal regularity estimates in the $L_p$-in-time and $L_q$-in-space setting by applying the Weis's operator valued Fourier multiplier theorem. |
| title | $\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space |
| topic | Analysis of PDEs 35Q35, 76N10 |
| url | https://arxiv.org/abs/2409.08457 |