论文标题
本杰明（Benjamin）和灯塔的尖锐版本，构成稳定的波浪
A sharp version of the Benjamin and Lighthill conjecture for steady waves with vorticity
论文作者
论文摘要
我们证明了所有二维稳态水波和任意涡度分布的所有二维稳态水波的刺想。我们表明，任意平滑波的流动力常数由共轭层流的相应流动常数界定。我们证明了这些不平等现象，没有任何关于表面轮廓几何形状的假设，并且对波幅度没有任何限制。此外，我们对何时发生平等的情况进行了完整的描述。我们的结果已经是涡度波动的新结果，而平等的情况即使在无关环境中也是新的。除了证明本杰明和灯塔猜想外，我们还为表面剖面建立了鲜明的界限，从而在二维稳定水波上扩大了先前的结果。
We prove the Benjamin and Lighthill conjecture for all two-dimensional steady water waves with an arbitrary vorticity distribution. We show that the flow force constant of an arbitrary smooth wave is bounded by the corresponding flow force constants for conjugate laminar flows. We prove these inequalities without any assumptions on the geometry of the surface profile and put no restrictions on wave's amplitude. Furthermore, we give a complete description of cases when equalities can occur. Our results are new already for Stokes waves with vorticity, while the case of equalities is new even in the irrotational setting. Beside proving the Benjamin and Lighthill conjectrure, we establish sharp bounds for the surface profile, extending previous results on two-dimensional steady water waves.
