论文标题
改善了本杰明和灯塔的猜想
Improved bound in the Benjamin and Lighthill conjecture
论文作者
论文摘要
关于稳态水波的经典本杰明和灯光猜想指出，溶液的非二维流动力常数分别由超临界和亚临界均匀流的相应常数。这些不平等决定了涵盖所有稳定运动的参数区域。实际上，并非该区域的所有点都决定了稳定波。在本说明中，我们证明了流动力常数的新的明确的下限，从某种意义上说，它在某种意义上是渐近的。特别是，对于弗洛德数量，这恢复了众所周知的不等式f <2，同时显着降低了支持稳定波的参数区域。
The classical Benjamin and Lighthill conjecture about steady water waves states that the non-dimensional flow force constant of a solution is bounded by the corresponding constants of the supercritical and subcritical uniform streams respectively. These inequalities determine a parameter region that covers all steady motions. In fact not all points of the region determine a steady wave. In this note we prove a new and explicit lower bound for the flow force constant, which is asymptotically sharp in a certain sense. In particular, this recovers the well known inequality F<2 for the Froude number, while significantly reducing the parameter region supporting steady waves.
