论文标题
Biharmonic NLS的圆柱对称解决方案的爆炸
Blowup of cylindrically symmetric solutions for biharmonic NLS
论文作者
论文摘要
在本文中，我们考虑了以下双式非线性schrödinger方程（NLS），$$ \ textnormal {i} \，\ partial_t u = epartial_t u =Δ其中$ d \ geq 1 $，$μ\ in \ r $和$ 0 <σ<\ infty $如果$ 1 \ leq d \ leq 4 $和$ 0 <σ<4/（d-4）$如果$ d \ geq 5 $。在质量关键和超临界情况下，我们确定了圆柱对称数据问题的爆炸解决方案。结果将已知的解决方案扩展到径向对称数据的问题。
In this paper, we consider blowup of solutions to the Cauchy problem for the following biharmonic nonlinear Schrödinger equation (NLS), $$ \textnormal{i} \, \partial_t u=Δ^2 u-μΔu-|u|^{2 σ} u \quad \text{in} \,\, \R \times \R^d, $$ where $d \geq 1$, $μ\in \R$ and $0<σ<\infty$ if $1 \leq d \leq 4$ and $0<σ<4/(d-4)$ if $d \geq 5$. In the mass critical and supercritical cases, we establish the existence of blowup solutions to the problem for cylindrically symmetric data. The result extends the known ones with respect to blowup of solutions to the problem for radially symmetric data.
