Small data blow-up for a system of nonlinear Schrödinger equations
Small data blow-up for a system of nonlinear Schrödinger equations
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DOI：
10.1016/j.jmaa.2012.10.003
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发表时间：
2012-10
影响因子：
1.3
通讯作者：
T. Ozawa;Hideaki Sunagawa
中科院分区：
文献类型：
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作者：
T. Ozawa;Hideaki Sunagawa
我们给出了一维空间中三分量二次非线性薛定谔方程组的小数据爆破的例子。我们的爆破解决方案的建设是基于Hopf-Cole变换，这使我们能够减少问题，以获得合适的增长估计的解决方案的转换系统。简化系统中的放大与质量共振密切相关。
We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf–Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.