Instabilities for supercritical Schr\"odinger equations in analytic manifolds
Instabilities for supercritical Schr\"odinger equations in analytic manifolds
复制标题
解析流形中超临界薛定格方程的不稳定性
DOI：
10.1016/j.jde.2007.12.001
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Laurent Thomann
中科院分区：
文献类型：
--
作者：
Laurent Thomann
本文考虑解析黎曼流形（Md,g）中的超临界非线性Schrödinger方程，其中度规g是解析的。利用解析的WKB方法，我们能够构造与时间无关的半经典方程的Ansatz。这些近似解将有助于显示两种不同类型的不稳定性。第一个是在能量空间，第二个是在更高的索博列夫范数下立即失去规律性。
In this paper we consider supercritical nonlinear Schrödinger equations in an analytic Riemannian manifold (Md,g), where the metric g is analytic. Using an analytic WKB method, we are able to construct an Ansatz for the semiclassical equation for times independent of the small parameter. These approximate solutions will help to show two different types of instabilities. The first is in the energy space, and the second is an immediate loss of regularity in higher Sobolev norms.