论文标题
一阶段不稳定的麝香问题严格的薄膜近似
Rigorous thin film approximations of the one-phase unstable Muskat problem
论文作者
论文摘要
本文研究了由重力和表面张力驱动的单相麝香问题。这里考虑的政权在干燥区域的顶部的流体不稳定。通过一种使用深度平均配方的新方法，我们在这种情况下得出了两个渐近近似。较低的近似值是经典的薄膜方程，而高阶近似值提供了新的精制薄膜方程。我们证明了两个模型具有低规范初始数据的模型的浅参数中的最佳收敛顺序。
This paper studies the one-phase Muskat problem driven by gravity and surface tension. The regime considered here is unstable with the fluid on top of a dry region. By a novel approach using a depth-averaged formulation, we derive two asymptotic approximations for this scenario. The lower order approximation is the classical thin film equation, while the higher order approximation provides a new refined thin film equation. We prove the optimal order of convergence in the shallowness parameter to the original Muskat solutions for both models with low-regular initial data.
