Strichartz Estimates and Applications to Semilinear Dispersive Equations
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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.
KeywordsWave Equation Sobolev Embedding Cauchy Data Strichartz Estimate Fourier Integral Operator
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