论文标题
Maxwell-Stefan-Cahn-Hilliard Systems的存在和虚弱的独特性
Existence and weak-strong uniqueness for Maxwell-Stefan-Cahn-Hilliard systems
论文作者
论文摘要
分析了一种根据Cahn-Hilliard型化学势的麦克斯韦 - 史丹系统与驱动力的流体混合物。相应的抛物线交叉扩散方程包含第四阶导数，并在无升华边界条件的有限域中考虑。分析的主要困难是扩散矩阵的退化，这可以通过证明子空间上矩阵的正确定性并使用Bott-Duffin矩阵倒数来克服。通过（相对）能量和熵估计值的仔细组合显示出弱解决方案的全球存在和弱浓度的唯一性能，从而产生了密度的$ H^2（ω）$界限，这是无法单独从能量或熵不等式获得的。
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a bounded domain with no-flux boundary conditions. The main difficulty of the analysis is the degeneracy of the diffusion matrix, which is overcome by proving the positive definiteness of the matrix on a subspace and using the Bott--Duffin matrix inverse. The global existence of weak solutions and a weak-strong uniqueness property are shown by a careful combination of (relative) energy and entropy estimates, yielding $H^2(Ω)$ bounds for the densities, which cannot be obtained from the energy or entropy inequalities alone.
