论文标题
汉堡 - 希尔伯特方程的不稳定冲击形成
Unstable shock formation of the Burgers-Hilbert equation
论文作者
论文摘要
本文证明了Arxiv：2006.05568中汉堡方程的不稳定冲击。更确切地说，我们使用有限的$ h^9 $ norm构建平滑的初始数据，以使自相似坐标中的解决方案渐近地对第一个不稳定的解决方案对自我相似的Inviscid burgers方程。爆炸配置文件是带有Hölder1/5连续性的风口，具有明确的爆炸时间和位置。与先前确定的稳定冲击不同，初始数据不能以空旷的方式获取；取而代之的是，我们通过牛顿的迭代来控制两个不稳定的方向。
This paper proves the existence of unstable shocks of the Burgers-Hilbert equation conjectured in arXiv:2006.05568. More precisely, we construct smooth initial data with finite $H^9$-norm such that the solution in self-similar coordinates is asymptotic to the first unstable solution to the self-similar inviscid Burgers equation. The blowup profile is a cusp with Hölder 1/5 continuity with explicit blowup time and location. Unlike the previously established stable shocks, the initial data cannot be taken in an open set; instead, we control the two unstable directions by Newton's iteration.
