论文标题
具有趋化和奇异潜力的Cahn-Hilliard-Navier-Stokes系统的全球弱解决方案
Global Weak Solutions to a Cahn-Hilliard-Navier-Stokes System with Chemotaxis and Singular Potential
论文作者
论文摘要
我们分析了一个漫射界面模型，该模型描述了具有趋化效果的不可压缩的两相流的动力学。 PDE系统将流体速度的Navier-Stokes方程式融合在一起，该方程是相位场变量的对流Cahn-Hilliard方程，并具有对养分密度的对流扩散反应方程。对于具有奇异潜力的系统，我们证明了在两个和三个维度中都存在全球弱解决方案。此外，在两个维度的情况下，我们建立了一个连续的依赖结果，暗示了全球弱解决方案的独特性。奇异电位保证了相位场变量在时间演化过程中始终保持在物理相关的间隔[-1,1]中。该属性使我们能够获得适当的结果，而无需对先前文献中的系数进行任何额外的假设。
We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the phase field variable with an advection-diffusion-reaction equation for the nutrient density. For the system with a singular potential, we prove the existence of global weak solutions in both two and three dimensions. Besides, in the two dimensional case, we establish a continuous dependence result that implies the uniqueness of global weak solutions. The singular potential guarantees that the phase field variable always stays in the physically relevant interval [-1,1] during time evolution. This property enables us to obtain the well-posedness result without any extra assumption on the coefficients that has been made in the previous literature.
