Remarks on scattering for nonlinear Schrödinger equations
Remarks on scattering for nonlinear Schrödinger equations
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DOI：
10.1007/s00030-002-8118-9
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发表时间：
2002-12
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影响因子：
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通讯作者：
K. Nakanishi;T. Ozawa
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文献类型：
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作者：
K. Nakanishi;T. Ozawa
统一了非线性薛定谔方程的两种不同的整体分析方法，即Sobolev空间和加权空间中的方法。因此，我们可以处理各种幂非线性项的和（1+2/n<p<），因为前者适用于，而后者适用于1+2/n<p。即使对于单次幂，我们的结果也比以前的结果简单得多，而且对初始数据的限制也稍好一些。此外，我们将结果扩展到最大正则性，从而获得在较低临界值$ p=1+8/（\sqrt{n^2+ 4 n +36}+n+2）\quad \textrm{for}\quad n\ge 4 $处的散射。我们还证明了在不存在小性的情况下，
We unify two distinct methods of the global analysis for the nonlinear Schrödinger equations, namely those in the Sobolev spaces and in the weighted spaces. Thus we can deal with various sums of power nonlineariesfor 1+2/n<p<, since the former works for, while the latter for 1+2/n<p. Even for a single power, our result is much simpler and slightly better than the previous ones as to restriction on the initial data. Moreover, we extend the result to the maximal regularity, thereby obtaining scattering at the lower critical value $ p=1+8/(\sqrt{n^2+4n+36}+n+2)\quad \textrm{for}\quad n\ge 4 $. We also show the asymptotic completeness inwithout smallness forand any.