论文标题
准压缩的两相流的局部良好性
Local Well-Posedness of a Quasi-Incompressible Two-Phase Flow
论文作者
论文摘要
我们显示了弥漫性界面模型的良好性，用于两种粘性不可压缩流体的两相流，其及时地局部具有不同的密度。该模型导致具有混合物的螺线管速度场的不均匀的Navier-Stokes/Cahn-Hilliard系统，但在Navier-Stokes型方程中流体混合物的可变密度可变。我们借助合适的线性化和收缩映射论点在本地证明了强大的解决方案。为此，我们显示了线性化系统的Stokes一部分的最大$ l^2 $ -REGUMALITY，并使用线性化的Cahn-Hilliard系统使用最大$ l^p $ -REGULATINE。
We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal velocity field for the mixture, but a variable density of the fluid mixture in the Navier-Stokes type equation. We prove existence of strong solutions locally in time with the aid of a suitable linearization and a contraction mapping argument. To this end we show maximal $L^2$-regularity for the Stokes part of the linearized system and use maximal $L^p$-regularity for the linearized Cahn-Hilliard system.
