论文标题
通用两相Stokes方程的解决方案及其在最大规律性上的应用；模型问题
Solution formula for generalized two-phase Stokes equations and its applications to maximal regularity; model problems
论文作者
论文摘要
在本文中，我们为两相Stokes方程提供了一个解决方案公式，在整个空间中具有和不具有平坦界面的表面张力和重力。解决方案公式已经由shibata-shimizu考虑。但是，我们重建该公式，以便我们能够证明解决方案的估计值和最大规律性估计值。在先前的工作中，他们需要在正常组件上假设其他条件。我们还要照顾正常的组件，而假设比以前弱。该方法基于$ h^\ infty $微积分，该微积分已经用于半空间中各种边界条件的Stokes问题。
In this paper we give a solution formula for the two-phase Stokes equations with and without surface tension and gravity in the whole space with flat interface. The solution formula has already considered by Shibata-Shimizu. However we reconstruct the formula so that we are able to prove resolvent estimate and maximal regularity estimate. In the previous work, they needed to assume additional conditions on normal components. We also take care of normal components, while the assumption becomes weaker than before. The method is based on an $H^\infty$ calculus which has already used for the Stokes problems with various boundary conditions in the half space.
