论文标题
自由边界不可压缩的弹性动力学与表面张力的局部良好性
Local Well-posedness of the Free Boundary Incompressible Elastodynamics with Surface Tension
论文作者
论文摘要
在本文中，我们考虑了不可压缩的Elatodynanigs的自由边界问题，这是流体运动的Euler方程的耦合系统，并带有用于变形张量的传输方程。在与表面张力的自由边界上的自然力量平衡定律下，我们在短时间间隔建立了其良好的度理论。我们的方法是通过对粘度建立统一的先验估计来消失的粘度极限。作为一种副产品，不可压缩的粘弹性的无粘性极限（系统与Navier-Stokes方程耦合）也是合理的。我们指出的是，基于对自由边界上弹性项固有结构的重要新观察，这里的框架仅在标准的Sobolev空间中建立，而不是\ cite {masrou}中使用的co normal space。
In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on the free boundary with the surface tension, we establish its well-posedness theory on a short time interval. Our method is the vanishing viscosity limit by establishing a uniform a priori estimates with respect to the viscosity. As a by-product, the inviscid limit of the incompressible viscoelasticity (the system coupling with the Navier-Stokes equations) is also justified. We point out that based on a crucial new observation of the inherent structure of the elastic term on the free boundary, the framework here is established solely in standard Sobolev spaces, but not the co-normal ones used in \cite{MasRou}.
