Weighted estimates for the Stokes semigroup in the half-space

Fuente: arXiv
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Main Authors: Di Feola, Angelica Pia, Pane, Vittorio
Format: Preprint
Published: 2025
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author Di Feola, Angelica Pia
Pane, Vittorio
author_facet Di Feola, Angelica Pia
Pane, Vittorio
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_06119
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Weighted estimates for the Stokes semigroup in the half-space
Di Feola, Angelica Pia
Pane, Vittorio
Analysis of PDEs
Mathematical Physics
35Q30, 35B65, 76D05
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.
title Weighted estimates for the Stokes semigroup in the half-space
topic Analysis of PDEs
Mathematical Physics
35Q30, 35B65, 76D05
url https://arxiv.org/abs/2508.06119