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)时, 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 Korteweg type in $\mathrm{\Omega }\text{sub}\text{R}3$. 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.