双流体系统中的大振幅内锋
Large-amplitude internal fronts in two-fluid systems
摘要：
在这份声明中，我们报告的结果存在的家庭的大幅度内部流体动力孔。这些是二维的完全两相不可压缩欧拉方程的行波解。流体的上下被水平的平面壁所限制，并受到重力的作用。我们得到连续曲线的解决方案，这个系统的分歧，从平凡的解决方案，界面是平坦的。随着这些族达到极限，内部界面要么翻转，要么与上壁接触，要么发展成高度退化的“双停滞”点。我们的建设是可能的一个新的抽象机制的整体延续的单调前型解决方案的椭圆型方程提出的无限圆柱。该理论是相当强大的，特别是，可以处理完全非线性方程以及准线性问题的传输边界条件。
英文摘要：
In this announcement, we report results on the existence of families of large-amplitude internal hydrodynamic bores. These are traveling front solutions of the full two-phase incompressible Euler equation in two dimensions. The fluids are bounded above and below by flat horizontal walls and acted upon by gravity. We obtain continuous curves of solutions to this system that bifurcate from the trivial solution where the interface is flat. Following these families to the their extreme, the internal interface either overturns, comes into contact with the upper wall, or develops a highly degenerate "double stagnation" point. Our construction is made possible by a new abstract machinery for global continuation of monotone front-type solutions to elliptic equations posed on infinite cylinders. This theory is quite robust and, in particular, can treat fully nonlinear equations as well as quasilinear problems with transmission boundary conditions.
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