论文标题
消失的粘度限制，用于与表面张力的可压缩粘弹性流体的自由边界问题
Vanishing viscosity limits for the free boundary problem of compressible viscoelastic fluids with surface tension
论文作者
论文摘要
我们考虑具有表面张力的可压缩等等递质粘弹性流体方程的自由边界问题。在自由边界上提出的物理动力学和动态条件下，我们研究了Sobolev空间中粘弹性流体方程的经典溶液的规律性，这些粘弹性方程在粘度上是均匀的，并证明了相应的消失粘度限制。我们证明的关键要素是，在拉格朗日坐标中的变形梯度张量可以用流量图表示为参数，因此弹性项的固有结构在消失的粘度的极限下提高了正常衍生物的均匀规律性。该结果表明，边界层没有出现在可压缩粘弹性流体的自由边界问题中，这与第二作者针对自由边界可压缩的Navier-Stokes系统所研究的情况不同。
We consider the free boundary problem of compressible isentropic neo-Hookean viscoelastic fluid equations with surface tension. Under the physical kinetic and dynamic conditions proposed on the free boundary, we investigate regularities of classical solutions to viscoelastic fluid equations in Sobolev spaces which are uniform in viscosity and justify the corresponding vanishing viscosity limits. The key ingredient of our proof is that the deformation gradient tensor in Lagrangian coordinates can be represented as a parameter in terms of flow map so that the inherent structure of the elastic term improves the uniform regularity of normal derivatives in the limit of vanishing viscosity. This result indicates that the boundary layer does not appear in the free boundary problem of compressible viscoelastic fluids which is different to the case studied by the second author for the free boundary compressible Navier-Stokes system.
