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Main Author: Higaki, Mitsuo
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.16079
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author Higaki, Mitsuo
author_facet Higaki, Mitsuo
contents We establish the first quantitative Runge approximation theorem, with explicit $L^2$-estimates, for the 3d nonstationary Stokes system on a bounded spatial domain. This result addresses the two primary limitations of the qualitative result [H.-Sueur, 2025] obtained in collaboration with Franck Sueur: first, it bypasses the non-constructive Hahn-Banach theorem used in [H.-Sueur, 2025], precluding quantitative estimates; and second, it extends the scope of the theory from interior approximations to the physically important initial-boundary value problem. Our proof is founded on the modern quantitative framework of [Rüland-Salo, 2019], which we adapt to the Stokes system by combining semigroup theory with a quantitative approximation for the associated resolvent problem.
format Preprint
id arxiv_https___arxiv_org_abs_2511_16079
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An $L^2$-quantitative global approximation for the Stokes initial-boundary value problem
Higaki, Mitsuo
Analysis of PDEs
We establish the first quantitative Runge approximation theorem, with explicit $L^2$-estimates, for the 3d nonstationary Stokes system on a bounded spatial domain. This result addresses the two primary limitations of the qualitative result [H.-Sueur, 2025] obtained in collaboration with Franck Sueur: first, it bypasses the non-constructive Hahn-Banach theorem used in [H.-Sueur, 2025], precluding quantitative estimates; and second, it extends the scope of the theory from interior approximations to the physically important initial-boundary value problem. Our proof is founded on the modern quantitative framework of [Rüland-Salo, 2019], which we adapt to the Stokes system by combining semigroup theory with a quantitative approximation for the associated resolvent problem.
title An $L^2$-quantitative global approximation for the Stokes initial-boundary value problem
topic Analysis of PDEs
url https://arxiv.org/abs/2511.16079