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Published in:
2011 | OriginalPaper | Chapter
Strichartz Estimates and Applications to Semilinear Dispersive Equations
Authors : Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
Published in: Fourier Analysis and Nonlinear Partial Differential Equations
Publisher: Springer Berlin Heidelberg
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Chapter 8 is devoted to
Strichartz estimates
for dispersive equations with a focus on Schrödinger and wave equations. After proving a dispersive inequality (i.e., decay in time of the
L
∞
norm in space) for these equations, we present, in a self-contained way, the celebrated
TT
⋆
argument based on a duality method and on bilinear estimates. Some examples of applications to semilinear Schrödinger and wave equations are given at the end of the chapter.