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Global well-posedness for Schr"odinger equation with derivative in $H^{{1/2}}(R)$ | | Changxing Miao
; Yifei Wu
; Guixiang Xu
; | | Date: |
23 Dec 2009 | | Abstract: | We consider the Cauchy problem of the cubic nonlinear Schr"odinger
equation with derivative in Sobolev spaces $H^s(R)$, which is known to
ill-posedness for $s<{1/2}$. In addition, I-term cite{CKSTT-01-DNLS},
cite{CKSTT-02-DNLS} obtained global well-posedness for $s>{1/2}$ by I-method.
While the endpoint case $s=1/2$ remained open. In this paper, we show that it
is global well-posedness in the endpoint space $H^{{1/2}}(R)$. The result
follows from the $I$-method with a "partial refined" argument. | | Source: | arXiv, 0912.4642 | | Services: | Forum | Review | PDF | Favorites | |
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