Maximal L_p-L_q regularity for the Stokes equations with various boundary conditions in the half space

2022/01/14 by Naoto Kajiwara, Kajiwara, Naoto
Computer Science · Mathematics · #35B45 #35D35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2201.05306

openalex publication_date 2022/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove resolvent L_p estimates and maximal L_p-L_q regularity estimates for the Stokes equations with Dirichlet, Neumann and Robin boundary conditions in the half space. Each solution is constructed by a Fourier multiplier of x'-direction and an integral of x_N-direction. We decompose the solution such that the symbols of the Fourier multipliers are bounded and holomorphic. We see that the operator norms are dominated by a homogeneous function of order -1 for x_N-direction. The basis are Weis's operator-valued Fourier multiplier theorem and a boundedness of a kernel operator. We give a new simple approach to get maximal regularity in the half space.

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