Analyticity of solutions to a quadratic system of Schr?dinger equations without mass resonance condition
Analyticity of solutions to a quadratic system of Schr?dinger equations without mass resonance condition
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无质量共振条件下薛定谔方程二次方程组解的解析性
DOI：
10.1016/j.jmaa.2018.07.009
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发表时间：
2018
影响因子：
1.3
通讯作者：
Hoshino Gaku
中科院分区：
文献类型：
--
作者：
Hoshino Gaku
本文研究了空间维数n≥ 4的二次薛定谔方程组的Cauchy问题，其中不满足质量共振条件.文献[14]研究了二次薛定谔方程组在质量共振条件下对指数衰减数据的解析光滑效应。在这项研究中，我们通过相位调制算子在解析哈代空间中构造整体解，基于尺度临界Sobolev空间H stecn/2− 2，具有类似于傅立叶超函数的测试函数的数据，条件是两个质量m1和m2之间的m1 ≤ m2 ≤（1+ 4/n）m1。
We consider the Cauchy problem for a quadratic system of Schrödinger equations in space dimensions n≥ 4 without mass resonance condition. Analytic smoothing effect for the quadratic system of Schrödinger equations under the mass resonance condition for data which satisfy exponentially decaying condition has been studied in [14]. In this study, we construct global solutions in the analytic Hardy space via the phase modulation operator, based on the scale critical Sobolev space H˙ n/2− 2 with data like the test functions of Fourier hyperfunctions, under the condition m 1≤ m 2≤(1+ 4/n) m 1 between two masses m 1 and m 2.