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| Autori principali: | , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2503.05352 |
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| _version_ | 1866910863529607168 |
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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 problem for the compressible fluid model of the Korteweg type, which is called the Navier-Stokes-Korteweg system, with surface tension in general domains. The Navier-Stokes-Korteweg system describes the liquid-vapor two-phase flow with non-zero thickness phase boundaries, which is often called the diffuse interface model. Our purpose is to show the solution operator families of the resolvent problem are $\mathcal R$-bounded, which gives us the generation of analytic semigroup and the maximal regularity in the $L_p$-in-time and $L_q$-in-space setting by applying the Weis operator valued Fourier multiplier theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05352 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $\mathcal R$-boundedness of solution operators for a compressible fluid model of Korteweg type in general domains Maryani, Sri Murata, Miho Analysis of PDEs In this paper, we consider a resolvent problem arising from the free boundary problem for the compressible fluid model of the Korteweg type, which is called the Navier-Stokes-Korteweg system, with surface tension in general domains. The Navier-Stokes-Korteweg system describes the liquid-vapor two-phase flow with non-zero thickness phase boundaries, which is often called the diffuse interface model. Our purpose is to show the solution operator families of the resolvent problem are $\mathcal R$-bounded, which gives us the generation of analytic semigroup and the maximal regularity in the $L_p$-in-time and $L_q$-in-space setting by applying the Weis operator valued Fourier multiplier theorem. |
| title | On the $\mathcal R$-boundedness of solution operators for a compressible fluid model of Korteweg type in general domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.05352 |