论文标题
关于不可压缩二进制流体的质量支持的艾伦-CAHN近似
On the Mass-Conserving Allen-Cahn Approximation for Incompressible Binary Fluids
论文作者
论文摘要
本文致力于在有限的平滑域$ω\ subset \ subset \ mathbb {r}^d $，$ d = 2,3 $的情况下，在存在毛细血管效应的情况下，在存在毛细血管效应的情况下，在存在毛细血管效应的情况下建模不可压缩的两相流体混合物的运动的全局良好性。我们专注于源自质量支持的Allen-CAHN动力学的耗散混合效应，具有与物理相关的Flory-Huggins潜力。更确切地说，我们研究了用于非均匀流体的质量支持的Navier-Stokes-Stokes-Stokes-Stokes-Stokes-allen-Cahn系统，以及用于均匀液体的质量持续的Euler-Allen-Cahn系统。我们证明了全球弱和强大解决方案的存在和独特性及其与纯国分离的特性。在我们的分析中，我们结合了能量和熵估计值，这是对两个函数的乘积的新终点估计，这是针对非稳定粘度的Stokes问题的新估计值，以及对数类型的Gronwall参数。
This paper is devoted to the global well-posedness of two Diffuse Interface systems modeling the motion of an incompressible two-phase fluid mixture in presence of capillarity effects in a bounded smooth domain $Ω\subset \mathbb{R}^d$, $d=2,3$. We focus on dissipative mixing effects originating from the mass-conserving Allen-Cahn dynamics with the physically relevant Flory-Huggins potential. More precisely, we study the mass-conserving Navier-Stokes-Allen-Cahn system for nonhomogeneous fluids and the mass-conserving Euler-Allen-Cahn system for homogeneous fluids. We prove existence and uniqueness of global weak and strong solutions as well as their property of separation from the pure states. In our analysis, we combine the energy and entropy estimates, a novel end-point estimate of the product of two functions, a new estimate for the Stokes problem with non-constant viscosity, and logarithmic type Gronwall arguments.
