Weighted Strichartz Estimates for the Radial Perturbed Schr?dinger Equation on the Hyperbolic Space

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• 作者：Vittoria Pierfelice
• 刊名：manuscripta mathematica
• 出版年：2006
• 出版时间：August, 2006
• 年：2006
• 卷：120
• 期：4
• 页码：377-389
• 全文大小：148 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

In this paper, we study the radial Schr?dinger equation perturbed with a rough time dependent potential on the hyperbolic space. It is natural to expect that the curvature of the manifold has some influence on the dispersive properties, indeed we obtain the weighted Strichartz estimates for the perturbed Cauchy problem. We shall notice that our weighted Strichartz estimates makes possible to treat the nonlinearity of the form g(Ω, u) which are unbounded as |Ω| → ∞.