Norm inflation for equations of KdV type with fractional dispersion
Norm inflation for equations of KdV type with fractional dispersion
复制标题
具有分数色散的 KdV 型方程的范数膨胀
DOI：
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发表时间：
2017
影响因子：
1.4
通讯作者：
V. M. Hur
中科院分区：
文献类型：
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作者：
V. M. Hur
我们证明了非线性非局部方程的范数膨胀，它扩展了Korteweg-de弗里斯方程，允许分数色散，在周期和非周期设置。也就是说，初始数据在Sobolev空间中是光滑的且任意小，但是在任意短的时间之后，解在Sobolev空间中变得任意大。
We demonstrate norm inflation for nonlinear nonlocal equations, which extend the Korteweg-de Vries equation to permit fractional dispersion, in the periodic and non-periodic settings. That is, an initial datum is smooth and arbitrarily small in a Sobolev space, but the solution becomes arbitrarily large in the Sobolev space after an arbitrarily short time.