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

2025/03/07 by Maryani, Sri, Murata, Miho
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.05352

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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