On the $\mathcal R$-boundedness of solution operators for a compressible fluid model of Korteweg type in general domains

Sri Maryani; Miho Murata

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arXiv · 2503.05352

On the $\mathcal R$-boundedness of solution operators for a compressible fluid model of Korteweg type in general domains

Sri Maryani·Miho Murata

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Abstract

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.

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BibTeX RIS

Sri Maryani, Miho Murata. 2025-03-07. On the $\mathcal R$-boundedness of solution operators for a compressible fluid model of Korteweg type in general domains. https://arxiv.org/abs/2503.05352

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