论文标题
热力学上一致的Navier-Stokes--cahn--Hilliard模型的分析
Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
论文作者
论文摘要
在本文中，在[18]中引入的热力学一致的Navier（cahn--Hilliard模型）中存在广义解决方案。广义的可溶性概念是衡量标准和耗散解决方案的。测量值配方包含熵不平等和能量不等式，而不是在当今的标准方式中，而不是能量平衡，内部变量的梯度流在弱的情况下实现，而动量平衡在衡量标准的意义上。在耗散公式中，动量平衡，能量以及熵不平等的分布关系被相对能量不平等取代。此外，我们证明了所提出的解决方案概念的弱唯一性，并且所有具有额外规律性的通用解决方案确实是强大的解决方案。
In this paper, existence of generalized solutions to a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model introduced in [18] is proven in any space dimension. The generalized solvability concepts are measure-valued and dissipative solutions. The measure-valued formulation incorporates an entropy inequality and an energy inequality instead of an energy balance in a nowadays standard way, the Gradient flow of the internal variable is fulfilled in a weak and the momentum balance in a measure-valued sense. In the dissipative formulation, the distributional relations of the momentum balance and the energy as well as entropy inequality are replaced by a relative energy inequality. Additionally, we prove the weak-strong uniqueness of the proposed solution concepts and that all generalized solutions with additional regularity are indeed strong solutions.
