Weighted estimates for the Stokes semigroup in the half-space

2025/08/08 by Angelica Pia Di Feola, Di Feola, Angelica Pia, Vittorio Pane +1
Computer Science · Engineering · Mathematics · #35B65 #35Q30 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.06119

openalex publication_date 2025/08/08 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

We investigate the initial-boundary value problem for the Stokes system in the half-space, within the framework of weighted Lebesgue spaces. Introducing a new weight function defined via a product of powers of distances from fixed points, we establish existence, uniqueness, and regularity results for strong solutions to the Stokes problem in the half space. Our analysis generalizes previous results for the Stokes system in radial-weighted spaces (Galdi and Maremonti, J. Math. Fluid Mech. 25:7,2023; Maremonti and Pane, J. Math. Fluid Mech. 27:2,2025) and extends the theory to our setting. These results represent a first step toward the analysis of the Navier-Stokes system in weighted spaces, with applications in both half-space and exterior domain configurations.

Citations

• The Navier-Stokes Cauchy problem in a class of weighted function spaces
• Weighted norm inequalities for convolution and Riesz potential

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