DYNAMICS OF COMPRESSIBLE NON-ISOTHERMAL FLUIDS OF NON-NEWTONIAN KORTEWEG TYPE

The equations of motion for compressible fluids of Korteweg type as derived by Dunn and Serrin in 1985 are studied in their full generality: the Korteweg tensor is assumed to be an arbitrary function of the form K := (-rho(2)partial derivative(rho)psi vertical bar rho del . (kappa del rho)) I - kappa del rho circle times del rho, kappa := 2 rho partial derivative(phi)psi(rho, theta, phi), phi := |del rho|(2), where psi denotes Helmholtz free energy density and the capillarity kappa is subject only to the natural positivity conditions kappa(rho,theta,phi) > 0, kappa(rho, theta, phi)+2 phi partial derivative(phi)kappa(rho, theta, phi) > 0, rho, theta, phi >= 0. The viscous stress is supposed to be of generalized Newtonian type. The main result of the paper establishes well-posedness on domains with compact boundaries; the proof is based on refined methods of maximal regularity.