Weighted estimates for the Stokes semigroup in the half-space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915545480167424 |
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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 |
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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 |