论文标题
具有二次相互作用的非线性Schrödinger方程系统的爆炸结果
Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction
论文作者
论文摘要
我们为在各向异性空间中具有二次相互作用的NLS方程系统建立爆炸结果。我们精确地显示了有限的时间爆破或呈圆柱形对称溶液的长期爆炸。随着我们的构建，我们证明了在质量批评的情况下，全球溶液动能的某些多项式下限，这又意味着沿任何不同的时间顺序逐渐逐步逐步逐步逐步逐步逐步逐步逐步逐步逐步逐步增长。我们的分析扩展到具有二次相互作用的一般NLS系统，并且还提供了径向案例中已知结果的改进。
We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetric solutions. With our construction, we moreover prove some polynomial lower bounds on the kinetic energy of global solutions in the mass-critical case, which in turn implies grow-up along any diverging time sequence. Our analysis extends to general NLS systems with quadratic interactions, and it also provides improvements of known results in the radial case.
