Low regularity well-posedness for the viscous surface wave equation

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（10）
• 页码范围: 1887-1924
• 页数: 38页
• 语种: 英文

摘要

In this paper,we prove the local well-posedness of the viscous surface wave equation in low regularity Sobolev spaces.The key points are to establish several new Stokes estimates depending only on the optimal boundary regularity and to construct a new iteration scheme on a known moving domain.Our method could be applied to some other fluid models with free boundaries.