Angled Crested Like Water Waves with Surface Tension II: Zero Surface Tension Limit

IF 2 4区数学 Q1 MATHEMATICS Memoirs of the American Mathematical Society Pub Date : 2024-01-01 DOI:10.1090/memo/1458

Siddhant Agrawal

引用次数: 0

Abstract

This is the second paper in a series of papers analyzing angled crested like water waves with surface tension. We consider the 2D capillary gravity water wave equation and assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. In the first paper \cite{Ag19} we constructed a weighted energy which generalizes the energy of Kinsey and Wu \cite{KiWu18} to the case of non-zero surface tension, and proved a local wellposedness result. In this paper we prove that under a suitable scaling regime, the zero surface tension limit of these solutions with surface tension are solutions to the gravity water wave equation which includes waves with angled crests.

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带表面张力的角峰状水波 II：零表面张力极限

本文是分析具有表面张力的角峰状水波系列论文的第二篇。我们考虑了二维毛细重力水波方程，并假设流体是不粘性、不可压缩、不可旋转的，且空气密度为零。在第一篇论文 \cite{Ag19}中，我们构造了一种加权能量，它将 Kinsey 和 Wu \cite{KiWu18}的能量推广到了表面张力不为零的情况，并证明了一个局部井放置性结果。在本文中，我们证明了在合适的缩放机制下，这些有表面张力的解的零表面张力极限是重力水波方程的解，其中包括有角度波峰的波。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.

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