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

This paper proves the existence of R$$ \mathcal{R} $$‐bounded solution operator families of the resolvent problem of Navier–Stokes–Korteweg model in half‐space (R+N)$$ \left({\mathbf{R}}_{+}^N\right) $$ with slip boundary condition. Especially we investigate the model for arbitrary constant viscosity and capillarity. We employ the R$$ \mathcal{R} $$‐bounded solution operators of the model obtained from the whole space cases and partial Fourier transform techniques to analyze the model. [ABSTRACT FROM AUTHOR]