{"title":"Determination of Time Dependent Source Terms for Stokes Systems in Unbounded Domains","authors":"Adel Blouza, Léo Glangetas, Yavar Kian, Van-Sang Ngo","doi":"10.1007/s00021-025-00996-2","DOIUrl":null,"url":null,"abstract":"<div><p>This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general class of time-dependent and vector-valued source terms with potentially unknown divergence. Taking into account the challenges inherent in this class of inverse source problems, we aim to identify the most precise conditions that ensure their resolution. Motivated by various fluid motion problems, we explore several class of boundary measurements. Our proofs are based on different arguments, including unique continuation properties for Stokes systems, approximate controllability, complex analysis, and the application of explicit harmonic functions and explicit solutions for Stokes systems. This analysis is complemented by a reconstruction algorithm and examples of numerical computations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 2","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2026-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-025-00996-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This article is devoted to the analysis of inverse source problems for Stokes systems in unbounded domains where the corresponding velocity flow is observed on a surface. Our main objective is to study the unique determination of general class of time-dependent and vector-valued source terms with potentially unknown divergence. Taking into account the challenges inherent in this class of inverse source problems, we aim to identify the most precise conditions that ensure their resolution. Motivated by various fluid motion problems, we explore several class of boundary measurements. Our proofs are based on different arguments, including unique continuation properties for Stokes systems, approximate controllability, complex analysis, and the application of explicit harmonic functions and explicit solutions for Stokes systems. This analysis is complemented by a reconstruction algorithm and examples of numerical computations.
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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