Local Solvability for a Compressible Fluid Model of Korteweg Type on General Domains

In this paper, we consider a compressible fluid model of the Korteweg type on general domains in the N -dimensional Euclidean space for N ≥ 2 . The Korteweg-type model is employed to describe fluid capillarity effects or liquid–vapor two-phase flows with phase transition as a diffuse interface model. In the Korteweg-type model, the stress tensor is given by the sum of the standard viscous stress tensor and the so-called Korteweg stress tensor, including higher order derivatives of the fluid density. The local existence of strong solutions is proved in an L p -in-time and L q -in-space setting, p ∈ ( 1 , ∞ ) and q ∈ ( N , ∞ ) , with additional regularity of the initial density on the basis of maximal regularity for the linearized system.