Blow-up solutions for the inhomogeneous Schrödinger equation with L2 supercritical nonlinearity
Blow-up solutions for the inhomogeneous Schrödinger equation with L2 supercritical nonlinearity
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DOI：
10.1016/j.jmaa.2013.07.029
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发表时间：
2014-01
影响因子：
1.3
通讯作者：
Shihui Zhu
中科院分区：
文献类型：
--
作者：
Shihui Zhu
本文研究了具有 L 2 超临界非线性的非齐次薛定谔方程的爆炸解。根据 Strauss (1977)[22] 中 Strauss 的论点，我们发现了径向对称函数的一个新的紧性引理。因此，我们用它来推导两个广义 Gagliardo-Nirenberg 型不等式的最佳常数。此外，我们获得了更精确尖锐的爆炸和全局存在性判据，并通过变分法推导了爆炸解的弱集中现象。
This paper studies blow-up solutions for the inhomogeneous Schrödinger equation with L 2 supercritical nonlinearity. In terms of Strauss’ arguments in Strauss (1977)[22], we find a new compactness lemma for radial symmetric functions. Thus, we use it to derive the best constants of two generalized Gagliardo–Nirenberg type inequalities. Moreover, we obtain a more precisely sharp criteria of blow-up and global existence, and derive the weak concentration phenomenon of blow-up solutions by the variational methods.