论文标题
对于1D周期性nls的全球存在的必要条件，具有非距离不变的二次非线性
Necessary and sufficient condition for global existence of $L^2$ solutions for 1D periodic NLS with non-gauge invariant quadratic nonlinearity
论文作者
论文摘要
我们在圆环上研究具有非规格不变二次非线性的1D NLS。库奇问题承认了相对于空间持续不变的微不足道的全球解决方案。仅通过关注傅立叶$ 0 $解决方案模式的行为，还研究了全球解决方案的不存在。但是，较早的作品不足以获得库奇问题全球存在的精确标准。在本文中，通过研究傅立叶$ 0 $模式与解决方案振荡之间的相互作用来显示全球存在的确切标准。也就是说，如果$ l^2 $解决方案与琐碎的解决方案不同。
We study 1D NLS with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global solutions which are constant with respect to space. The non-existence of global solutions also has been studied only by focusing on the behavior of the Fourier $0$ mode of solutions. However, the earlier works are not sufficient to obtain the precise criteria for the global existence for the Cauchy problem. In this paper, the exact criteria for the global existence of $L^2$ solutions is shown by studying the interaction between the Fourier $0$ mode and oscillation of solutions. Namely, $L^2$ solutions are shown a priori not to exist globally if they are different from the trivial ones.
