论文标题
升级标准以下缩放标准，用于散入能量强度的NLS和定量的全局散射边界
Blow-up criteria below scaling for defocusing energy-supercritical NLS and quantitative global scattering bounds
论文作者
论文摘要
我们在径向对称解决方案的缩放阈值下方建立了定量爆破标准，该解决方案使用非线性$ | u |^6u $ defocting depotoctric symmetric解决方案。这为我们的知识提供了第一个通用结果，从而区分了散焦方程的潜在爆破解决方案与聚焦案例中许多已知的爆炸示例。我们的主要工具是结果的定量版本，显示基于$ l^2 $的关键Sobolev规范的统一范围意味着散射估计值。 作为我们技术的另一种应用，我们建立了一种变体，该变体可以使临界规范缓慢增长。我们表明，如果紧凑的时间间隔的临界Sobolev规范受到缓慢增长的数量来控制的，则取决于Stricharz Norm，则可以在全球范围内扩展溶液，并具有相应的散射估算。
We establish quantitative blow-up criteria below the scaling threshold for radially symmetric solutions to the defocusing nonlinear Schrödinger equation with nonlinearity $|u|^6u$. This provides to our knowledge the first generic results distinguishing potential blow-up solutions of the defocusing equation from many of the known examples of blow-up in the focusing case. Our main tool is a quantitative version of a result showing that uniform bounds on $L^2$-based critical Sobolev norms imply scattering estimates. As another application of our techniques, we establish a variant which allows for slow growth in the critical norm. We show that if the critical Sobolev norm on compact time intervals is controlled by a slowly growing quantity depending on the Stricharz norm, then the solution can be extended globally in time, with a corresponding scattering estimate.
