R-Bounded Operator Families Arising from a Compressible Fluid Model of Korteweg Type with Surface Tension in the Half-Space.

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 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 (Weis in Math Ann 319:735–758, 2001). [ABSTRACT FROM AUTHOR]