Applications of the Green tensor estimates of the nonstationary Stokes system in the half space

2024/07/09 by Kyungkeun Kang, Baishun Lai, Kang, Kyungkeun +5
Earth and Planetary Sciences · Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Vibration Analysis #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Spacecraft and Cryogenic Technologies

paper · pdf · doi:10.48550/arxiv.2407.07001

openalex publication_date 2024/07/09 · openalex created_date 2024/07/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a series of applications of the pointwise estimates of the (unrestricted) Green tensor of the nonstationary Stokes system in the half space, established in our previous work [CMP 2023]. First, we show the L¹-L^q estimates for the Stokes flow with possibly non-solenoidal L¹ initial data, generalizing the results of Giga-Matsui-Shimizu [Math. Z. 1999] and Desch-Hieber-Prüss [J. Evol. Equ. 2001]. Second, we construct mild solutions of the Navier-Stokes equations in the half space with mixed-type pointwise decay or with pointwise decay alongside boundary vanishing. Finally, we explore various coupled fluid systems in the half space including viscous resistive magnetohydrodynamics equations, a coupled system for the flow and the magnetic field of MHD type, and the nematic liquid crystal flow. For each of these systems, we construct mild solutions in L^q, pointwise decay, and uniformly local L^q spaces.

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