2014 | OriginalPaper | Buchkapitel
An inverse Strichartz inequality
verfasst von : Herbert Koch, Daniel Tataru, Monica Vişan
Erschienen in: Dispersive Equations and Nonlinear Waves
Verlag: Springer Basel
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In this section, we develop tools that we will employ to prove a linear profile decomposition for the Schrödinger propagator for bounded sequences in
$$\dot{H}^{1}(\mathbb{R}^{d})$$
with
d
≥ 3. Such a linear profile decomposition was first obtained by Keraani [18], relying on an improved Sobolev inequality proved by Gérard, Meyer, and Oru [16]. We should also note the influential precursor [1], which treated the wave equation. In these notes we present a different proof of the result in [18], which relies instead on an inverse Strichartz inequality.