论文标题
毛细血管驱动的Stokes流量：单相问题是小粘度极限
Capillarity driven Stokes flow: the one-phase problem as small viscosity limit
论文作者
论文摘要
我们考虑了排序的Stokes流，该流动描述了在无界的无限底几何形状中表面张力效应的影响下二维流体体的运动。我们将问题重新制定为一个完全非线性的抛物线进化问题，用于参数用以奇异积分表达的非线性来参数化流体的边界。我们证明了该问题在sobolev spaces $ h^s（\ mathbb {r}）$中的问题，并具有关键的规律性，并为解决方案建立了抛物线平滑属性。此外，当其中一种流体的粘度消失时，我们将问题确定为两相排序Stokes流动的单数极限。
We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear parabolic evolution problem for the function that parameterizes the boundary of the fluid with the nonlinearities expressed in terms of singular integrals. We prove well-posedness of the problem in the subcritical Sobolev spaces $H^s(\mathbb{R})$ up to critical regularity, and establish parabolic smoothing properties for the solutions. Moreover, we identify the problem as the singular limit of the two-phase quasistationary Stokes flow when the viscosity of one of the fluids vanishes.
