The existence of R$$ \mathcal{R} $$‐bounded solution operator for Navier–Stokes–Korteweg model with slip boundary conditions in half space

Abstract

This paper proves the existence of ‐bounded solution operator families of the resolvent problem of Navier–Stokes–Korteweg model in half‐space with slip boundary condition. Especially we investigate the model for arbitrary constant viscosity and capillarity. We employ the ‐bounded solution operators of the model obtained from the whole space cases and partial Fourier transform techniques to analyze the model.