$\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space

Sri Maryani; Miho Murata

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arXiv · 2409.08457

$\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space

Sri Maryani·Miho Murata

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Abstract

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.

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Sri Maryani, Miho Murata. 2024-09-13. $\mathcal R$-bounded operator families arising from a compressible fluid model of Korteweg type with surface tension in the half-space. https://arxiv.org/abs/2409.08457

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