On well-posedness for nonlinear Schrödinger equations with power nonlinearity in fractional order Sobolev spaces
On well-posedness for nonlinear Schrödinger equations with power nonlinearity in fractional order Sobolev spaces
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DOI：
10.1016/j.jmaa.2012.04.079
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发表时间：
2012-11
影响因子：
1.3
通讯作者：
H. Uchizono;Takeshi Wada
中科院分区：
文献类型：
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作者：
H. Uchizono;Takeshi Wada
研究了非线性薛定谔方程在R1+n中的适定性，其中p>；1，λ∈C，证明了(NLS)在HsiF2<；S<；4和S/2<；p<；1+4/(n−2s)+中局部适定.为了得到p的一个好的下界，我们系统地使用分数阶Besov空间中的Strichartz型估计。
We study the well-posedness for the nonlinear Schrödinger equation (NLS) in R1+n, where p>1,λ∈C, and prove that (NLS) is locally well-posed in Hsif 2<s<4 and s/2<p<1+4/(n−2s)+. To obtain a good lower bound for p, we systematically use Strichartz type estimates in fractional order Besov spaces for the time variable.