Low Regularity Solutions for Gravity Water Waves
Low Regularity Solutions for Gravity Water Waves
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重力水波的低规律性解决方案
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Albert Ai
中科院分区：
文献类型：
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作者：
Albert Ai
我们证明了无表面张力重力水波方程的局部适定性，初始速度场为$$H^s$$ Hs, $$s > frac{d}{2} + 1 - mu $$ s>d2+1-μ，其中$$d = 1$$ d=1时$$mu = frac{1}{10}$$ μ=110, $$d ge 2$$ d≥2时$$mu = frac{1}{5}$$ μ=15，推广了Alazard-Burq-Zuily的先前结果。这种改善主要体现在两个方面。首先，我们对欧拉坐标系到拉格朗日坐标系的变量变化规律进行了改进的分析。其次，我们对局部Strichartz估计进行了时间区间长度优化。
We prove local well-posedness for the gravity water waves equations without surface tension, with initial velocity field in $$H^s$$Hs, $$s > frac{d}{2} + 1 - mu $$s>d2+1-μ, where $$mu = frac{1}{10}$$μ=110 in the case $$d = 1$$d=1 and $$mu = frac{1}{5}$$μ=15 in the case $$d ge 2$$d≥2, extending previous results of Alazard–Burq–Zuily. The improvement primarily arises in two areas. First, we perform an improved analysis of the regularity of the change of variables from Eulerian to Lagrangian coordinates. Second, we perform a time-interval length optimization of the localized Strichartz estimates.