Endpoint Strichartz estimate for the damped wave equation and its application

2019/03/14 by Takahisa Inui, Inui, Takahisa, Yuta Wakasugi +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.05891

openalex publication_date 2019/03/14 · openalex created_date 2019/03/22 · openalex updated_date 2026/07/28

Abstract

Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz estimate in the wave endpoint case. We slightly modify the argument of Keel--Tao. Moreover, we apply the endpoint Strichartz estimate to the unconditional uniqueness for the energy critical nonlinear damped wave equation. This problem seems not to be solvable as the perturbation of the wave equation.

Citations

• Space‐time estimates for null forms and the local existence theorem

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