论文标题
可压缩的重力 - 毛细血管具有涡度：局部良好性，不可压缩且零色调的极限
Compressible Gravity-Capillary Water Waves with Vorticity: Local Well-Posedness, Incompressible and Zero-Surface-Tension Limits
论文作者
论文摘要
我们考虑3D可压缩的等质Euler方程，描述了一个无界初始域中具有移动边界和有限深度的固定平底底部的液体运动的运动。液体在重力和表面张力的影响下，并非被认为是无关的。我们通过结合精心设计的近似系统和双曲线方法来证明本地适合度，该方法使我们能够避免使用NASH-MOSER迭代。能量估计不产生规律性损失，并且在马赫数上是均匀的，并且在瑞利 - 泰勒标志条件下它们的表面张力系数均匀。因此，我们同时获得了不可压缩的表面张力限制。此外，我们可以通过将范例分化的积分应用于自由表面演化的分析，从而在高阶时间衍生物上删除均匀的界限（相对于马赫数）。
We consider 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and surface tension and it is not assumed to be irrotational. We prove local well-posedness by combining a carefully designed approximate system and a hyperbolic approach which allows us to avoid using Nash-Moser iteration. The energy estimates yield no regularity loss and are uniform in Mach number, and they are uniform in surface tension coefficient under the Rayleigh-Taylor sign condition. We thus simultaneously obtain incompressible and zero surface tension limits. Moreover, we can drop the uniform boundedness (with respect to Mach number) on high-order time derivatives by applying the paradifferential calculus to the analysis of the free-surface evolution.
