Generalized Strichartz estimates and scattering for 3D Zakharov system. (English) Zbl 1302.35336
The authors consider the Schrödinger type dispersive equations \(i \partial_t u +D^{a}u=0,\;u(0,x)=f(x)\), where \(u: \mathbb{R}\times \mathbb{R}^d \to \mathbb{C},\;D=\sqrt{-\Delta},\;a\neq 1\) for which they obtain generalized Strichartz estimates in the space of \(L^2\) angular integrable functions. These estimates are further used in the paper to show scattering for the \(3\)D Zakharov system with non-radial small initial data with certain angular regularity.
Reviewer: Alina Stancu (Montréal)
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q41 | Time-dependent Schrödinger equations and Dirac equations |
| 35B45 | A priori estimates in context of PDEs |
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