论文标题
在Cahn-Hilliard-navier-Stokes方程式上具有非均匀边界
On Cahn-Hilliard-Navier-Stokes equations with Nonhomogeneous Boundary
论文作者
论文摘要
有界域中的两个等温，不可压缩的，不可压缩的流体的演变由Cahn-Hilliard-Navier-Stokes方程（CHNS System）控制。在这项工作中，我们研究了CHNS系统具有非均匀边界条件的良好性结果。我们在二维有限域中获得了全局弱解的存在。我们进一步证明了解决方案对初始条件和边界数据的持续依赖性，这些条件和边界数据将提供弱解决方案的唯一性。这项工作还建立了强大解决方案的存在。此外，我们表明，在二维情况下，每个全局弱解决方案都会收敛到固定解决方案。
The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes equations (CHNS System). In this work, we study the well-posedness results for the CHNS system with nonhomogeneous boundary condition for the velocity equation. We obtain the existence of global weak solutions in the two-dimensional bounded domain. We further prove the continuous dependence of the solution on initial conditions and boundary data that will provide the uniqueness of the weak solution. The existence of strong solutions is also established in this work. Furthermore, we show that in the two-dimensional case, each global weak solution converges to a stationary solution.
