Strichartz estimates for equations with structured Lipschitz coefficients

2022/01/01 by Dorothee Frey, Robert Schippa, Frey, Dorothee +1
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques

paper · doi:10.48550/arxiv.2202.09260

openalex publication_date 2022/01/01 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Sharp Strichartz estimates are proved for Schrödinger and wave equations with Lipschitz coefficients satisfying additional structural assumptions. We use Phillips functional calculus as a substitute for Fourier inversion, which shows how dispersive properties are inherited from the constant-coefficient case. Global Strichartz estimates follow provided that the derivatives of the coefficients are integrable. The estimates extend to structured coefficients of bounded variations. As applications we derive Strichartz estimates with additional derivative loss for wave equations with Hölder-continuous coefficients and solve nonlinear Schrödinger equations. Finally, we record spectral multiplier estimates, which follow from the Strichartz estimates by well-known means.

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