论文标题
两流体系统中的大振幅内部前线
Large-amplitude internal fronts in two-fluid systems
论文作者
论文摘要
在此公告中，我们报告了大振幅内部流体动力孔的存在的结果。这些是整个两相不可压缩的Euler方程的前线溶液，分为两个维度。流体在平坦的水平壁上和下方界定，并通过重力作用。我们获得了该系统的连续曲线，这些曲线是从界面平坦的琐碎溶液中分叉的。跟随这些家庭的极端，内部界面要么翻转，要么与上壁接触，要么发展出高度退化的“双重停滞”点。 通过一种新的抽象机制，可以使单调前型解决方案全球延续到无限缸上的椭圆方程式。该理论非常健壮，尤其可以治疗完全非线性方程以及在传输边界条件下的准线性问题。
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.
