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The aim of this paper is to show the existence of $\mathcal{R}$-boundedsolution operator families for a generalized resolvent problem on thehalf-space arising from a compressible fluid model of Korteweg type. Such acompressible fluid model was derived by Dunn and Serrin (1985) and studied byKotschote (2008) as an initial-boundary value problem.

Existence of $\mathcal{R}$-bounded solution operator families for a compressible fluid model of Korteweg type on the half-space