具有渐逝岛或突现岛的湖泊方程
Lake equations with an evanescent or emergent island
摘要：
我们研究了湖方程在以下两种情况下的渐近动力学，一个岛屿收缩成一个点和一个新兴的岛屿。对于这两种情况，我们推导出一个渐近湖型方程。在前一种情况下，渐近动力学包括一个额外的狄拉克质量的涡。主要的数学困难是当水深为零时方程组奇异。我们在加权空间中对相关的流函数给出了新的一致估计，这将隐含紧性结果。
英文摘要：
We study the asymptotic dynamics of the lake equations in the following two cases, an island shrinking to a point and an emerging island. For both cases, we derive an asymptotic lake-type equation. In the former case, the asymptotic dynamics includes an additional Dirac mass in the vorticity. The main mathematical difficulty is that the equations are singular when the water depth vanishes. We provide new uniform estimates in weighted spaces for the related stream functions which will imply the compactness result.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
