Compressible fluid model of Korteweg type with free boundary condition: model problem

TL;DR

This paper establishes the existence of solution operator families for a resolvent problem related to a compressible Korteweg fluid model with free boundary conditions, extending previous boundary value problem analyses.

Contribution

It proves the existence of 5-bounded solution operators for a resolvent problem in a compressible Korteweg fluid model with free boundary conditions, a novel result in this context.

Findings

Existence of 5-bounded solution operator families

Extension of previous boundary value problem results

Application to compressible fluid models of Korteweg type

Abstract

The aim of this paper is to prove the existence of ${\mathcal R}$-bounded solution operator families for a resolvent problem on the upper half-space arising from a compressible fluid model of Korteweg type with free boundary condition. Such a compressible fluid model was derived by Dunn and Serrin (1985) and studied by Kotschote (2008) as a boundary value problem with non-slip boundary condition.