A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted L_p-space

2023/02/15 by Jae-Hwan Choi, Choi, Jae-Hwan, Ildoo Kim +3
Mathematics · #35B30 #35B65 #35S05 #47G30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2302.07507

openalex publication_date 2023/02/15 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/30

Abstract

In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm Lebesgue spaces. The class of temporal weights in our regularity estimates contains Muckenhoupt's class, and the initial data is in weighted Besov spaces with variable order.

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