SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 574-648, January 2021.
Consider the dynamics of a layer of viscous incompressible fluid under the influence of gravity. The upper boundary is a free boundary with the effect of surface tension taken into account, and the lower boundary is a fixed boundary on which the Navier slip condition is imposed. It is proved that there is a uniform time interval on which the estimates independent of both viscosity and surface tension coefficients of the solution can be established. This then allows one to justify the vanishing viscosity and surface tension limits by the strong compactness argument. In the presence of surface tension, the main difficulty lies in the less regularity of the highest temporal derivative of the mean curvature of the free surface and the pressure. It seems hard to overcome this difficulty by using the vorticity in viscous boundary layers. One of the key observations here is to find that there is a crucial cancelation between the mean curvature and the pressure by using the dynamic boundary condition.

中文翻译：

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不可压缩粘性表面波的消失粘度和表面张力极限

SIAM数学分析杂志，第53卷，第1期，第574-648页，2021年1月。
考虑重力作用下的粘性不可压缩流体层的动力学。上边界是考虑了表面张力影响的自由边界，下边界是施加了Navier滑动条件的固定边界。证明存在一个均匀的时间间隔，在该时间间隔上可以建立与溶液的粘度和表面张力系数无关的估计。然后，这可以通过强紧密性论证来证明消失的粘度和表面张力极限是合理的。在存在表面张力的情况下，主要困难在于自由表面的平均曲率和压力的最高时间导数的规律性较小。似乎很难通过使用粘性边界层中的涡旋来克服这一困难。