Global Well-Posedness for $$H^{-1}(\mathbb {R})$$ Perturbations of KdV with Exotic Spatial Asymptotics
Global Well-Posedness for $$H^{-1}(\mathbb {R})$$ Perturbations of KdV with Exotic Spatial Asymptotics
复制标题
$$H^{-1}(mathbb {R})$$ 具有奇异空间渐近的 KdV 扰动的全局适定性
DOI：
10.1007/s00220-022-04522-7
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发表时间：
2022
影响因子：
2.4
通讯作者：
Laurens, Thierry
中科院分区：
文献类型：
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作者：
Laurens, Thierry
给出实直线上Korteweg-de Vries方程的适当解V(t，x)，我们证明了初值的整体适定性。我们关于Vdo的条件包括正则性，但不对空间渐近性强加任何假设。我们证明了周期性轮廓证明了我们的假设。特别地，我们可以处理被广泛研究的KdV周期行波解(椭圆波)的局域扰动。在配套的论文Laurens(非线性.35(1)：343-387,2022年。Https://doi.org/10.1088/1361-6544/ac37f5)，我们证明了光滑阶梯状的初始数据也满足我们的假设。我们采用了Killip和VişAn(AN.数学课。(二)190(1)：249-305,2019年。Https://doi.org/10.4007/annals.2019.190.1.4)在哪里。在这种背景下，众所周知，空间的类别是尖锐的。
Given a suitable solutionV(t,x) to the Korteweg–de Vries equation on the real line, we prove global well-posedness for initial data. Our conditions onVdo include regularity but do not impose any assumptions on spatial asymptotics. We show that periodic profilessatisfy our hypotheses. In particular, we can treat localized perturbations of the much-studied periodic traveling wave solutions (cnoidal waves) of KdV. In the companion paper Laurens (Nonlinearity. 35(1):343–387, 2022. https://doi.org/10.1088/1361-6544/ac37f5) we show that smooth step-like initial data also satisfy our hypotheses. We employ the method of commuting flows introduced in Killip and Vişan (Ann. Math. (2) 190(1):249–305, 2019. https://doi.org/10.4007/annals.2019.190.1.4) where. In that setting, it is known thatis sharp in the class ofspaces.