Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations
Small data scattering for nonlinear Schrödinger wave and Klein-Gordon equations
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DOI：
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发表时间：
2002
影响因子：
1.4
通讯作者：
Makoto Nakamura;T. Ozawa
中科院分区：
文献类型：
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作者：
Makoto Nakamura;T. Ozawa
献给Giorgio Velo教授，在他六十岁生日之际。在全空间Rn（s < n/2）上的Sobolev空间中，研究了具有幂型非线性项的非线性Schrodinger方程（NLS）、非线性波动方程（NLW）和非线性Klein-Gordon方程（NLKG）的小数据点散射问题.非线性的假设是以幂次特性p1在0和p2在无穷大来描述的，例如对于NLS和NLKG为1 + 4/n ≤ p1 ≤ p2 ≤ 1 + 4/（n − 2s），对于NLW为1 + 4/（n − 1）≤ p1 ≤ p2 ≤ 1 + 4/（n − 2s）。
Dedicated to Professor Giorgio Velo on the occasion of his sixtieth birthday Abstract. Small data scattering for nonlinear Schrodinger equations (NLS), non- linear wave equations (NLW), nonlinear Klein-Gordon equations (NLKG) with power type nonlinearities is studied in the scheme of Sobolev spaces on the whole space R n with order s < n/2. The assumptions on the nonlinearities are described in terms of power behavior p1 at zero and p2 at infinity such as 1 + 4/n ≤ p1 ≤ p2 ≤ 1 + 4/(n − 2s) for NLS and NLKG, and 1 + 4/(n − 1) ≤ p1 ≤ p2 ≤ 1 + 4/(n − 2s) for NLW.