Singularities of Bernoulli Free Boundaries
Singularities of Bernoulli Free Boundaries
复制标题
伯努利自由边界的奇点
DOI：
10.1080/03605300600635012
复制
发表时间：
2006
影响因子：
1.9
通讯作者：
Eugen Varvaruca
中科院分区：
文献类型：
--
作者：
Eugen Varvaruca
在这篇文章中，我们证明了，对于一个大类的Bernoulli问题，一个自由边界，这是对称的垂直线通过一个孤立的奇点必须有一个角点，我们给出了一个公式的包含角。所用的假设承认在自由边界上可能存在其他奇点，甚至是无数个奇点。这一结果是水动力波理论中第一Stokes猜想的推广。我们还表明，即使在奇点的存在下，一个几何简单的伯努利自由边界必然是对称的。
In this article we show that, for a large class of Bernoulli problems, a free boundary which is symmetric with respect to a vertical line through an isolated singular point must necessarily have a corner at that point, and we give a formula for the contained angle. The assumptions used admit the possibility of other singular points, even uncountably many, on the free boundary. This result is an extension of the first Stokes conjecture in the theory of hydrodynamic waves. We also show that, even in the presence of singularities, a geometrically simple Bernoulli free boundary is necessarily symmetric.