Strong solutions for a compressible fluid model of Korteweg type

We prove existence and uniqueness of local strong solutions for a model of capillary compressible fluids derived by J.E. Dunn and J. Serrin (1985). This nonlinear problem is approached by proving maximal regularity for a related linear problem in order to formulate a fixed point equation, which is solved by the contraction mapping principle. Localising the linear problem leads to model problems in full and half space, which are treated by Dore-Venni-Theory, real interpolation and ${\cal H}^\infty$-calculus. For these steps, it is decisive to find conditions on the inhomogeneities being necessary and sufficient.