粘性系数依赖于密度的Korteweg型不可压流体的强解问题

Strong Solutions for the Incompressible Fluids of Korteweg Type with Density-Dependent Viscosity

研究一类Korteweg型不可压流体模型的强解问题.针对粘性系数依赖于密度的情形,当初始值满足兼容性条件(9)对,证明了强解的局部存在性和唯一性.我们在这指出,本文允许初始真空存在.

We study the strong solutions for the incompressible fluid models of Ko- rteweg type in Ω∪→ R^3. We focus on the case whese the viscosity coefficient depends on the density and prove the existence and uniqueness of local strong solutions provided the initial data satisfy a compatibility condition （see （9））. We point out here that in this paper we allow the initial vacuum to exist.