Blowup solutions for the nonlinear Schrödinger equation with complex coefficient
Blowup solutions for the nonlinear Schrödinger equation with complex coefficient
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DOI：
10.57262/die/1600135321
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发表时间：
2019-05
影响因子：
1.4
通讯作者：
Shota Kawakami;Shuji Machihara
中科院分区：
文献类型：
--
作者：
Shota Kawakami;Shuji Machihara
本文构造了一类系数为复数的具有幂非线性项的非线性薛定谔方程的有限时间爆破解。我们推广了Cazenave，Martel和Zhao \cite{CMZ}的结果的幂和复系数的范围.作为奖励，我们可以考虑空间维度5美元。我们显示了一系列的解决方案接近的爆破配置文件，这是一个爆破解决方案的常微分方程。我们应用Aubin-Lions引理来证明其收敛性。
We construct a finite time blow up solution for the nonlinear Schrodinger equation with the power nonlinearity whose coefficient is complex number. We generalize the range of both the power and the complex coefficient for the result of Cazenave, Martel and Zhao \cite{CMZ}. As a bonus, we may consider the space dimension $5$. We show a sequence of solutions closes to the blow up profile which is a blow up solution of ODE. We apply the Aubin-Lions lemma for the compactness argument for its convergence.