{"ID":2874633,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05287","arxiv_id":"2509.05287","title":"Inverse problem for the Navier-Stokes equations and identification of immersed obstacles in the Mediterranean Sea","abstract":"This paper presents a theoretical and numerical investigation of object detection in a fluid governed by the three-dimensional evolutionary Navier--Stokes equations. To solve this inverse problem, we assume that interior velocity measurements are available only within a localized subregion of the fluid domain. First, we present an identifiability result. We then formulate the problem as a shape optimization task: to identify the obstacle, we minimize a nonlinear least-squares criterion with a regularization term that penalizes the perimeter of the obstacle to be identified. We prove the existence and stability of a minimizer of the least-squares functional. To recover the unknown obstacle, we present a non-iterative identification method based on the topological derivative. The corresponding asymptotic expansion of the least-squares functional is computed in a straightforward manner using a penalty method. Finally, as a realistic application, we demonstrate the robustness and effectiveness of the proposed non-iterative procedure through numerical experiments using the INSTMCOTRHD ocean model, which incorporates realistic Mediterranean bathymetry, stratification, and forcing conditions.","short_abstract":"This paper presents a theoretical and numerical investigation of object detection in a fluid governed by the three-dimensional evolutionary Navier--Stokes equations. To solve this inverse problem, we assume that interior velocity measurements are available only within a localized subregion of the fluid domain. First, w...","url_abs":"https://arxiv.org/abs/2509.05287","url_pdf":"https://arxiv.org/pdf/2509.05287v1","authors":"[\"Mourad Hrizi\",\"Marwa Ouni\",\"Maatoug Hassine\"]","published":"2025-09-04T13:20:14Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.OC\"]","methods":"[]","has_code":false}