Publikation: Unique continuation of static overdetermined magnetohydrodynamic equations
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2025
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Rendiconti Lincei. Matematica e Applicazioni. European Mathematical Society (EMS) ; Accademia Nazionale dei Lincei, Roma, Classe di Scienze Fisiche, Matematiche e Naturali. 2025, 36(1), S. 3-33. ISSN 1120-6330. eISSN 1720-0768. Verfügbar unter: doi: 10.4171/rlm/1063
Zusammenfassung
This paper establishes the Unique Continuation Property (UCP) for a suitably overdetermined Magnetohydrodynamics (MHD) eigenvalue problem, which is equivalent to the Kalman, finite-rank, controllability condition for the finite-dimensional unstable projection of the linearized dynamic MHD problem. It is the “ignition key” to obtain uniform stabilization of the dynamic non-linear MHD system near an unstable equilibrium solution, by means of finitely many, interior, localized feedback controllers [Res. Math. Sci. 12 (2025), article no. 7]. The proof of the UCP result uses a pointwise Carleman-type estimate for the Laplacian following the approach that was introduced in [Nonlinear Anal. 71 (2009), 4967–4976] for the Navier–Stokes equations and further extended in [Appl. Math. Optim. 84 (2021), 2099–2146] for the Boussinesq system.
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510 Mathematik
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magnetohydrodynamics equations, unique continuation, uniform stabilization, Carleman estimates
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LASIECKA, Irena, Buddhika PRIYASAD, Roberto TRIGGIANI, 2025. Unique continuation of static overdetermined magnetohydrodynamic equations. In: Rendiconti Lincei. Matematica e Applicazioni. European Mathematical Society (EMS) ; Accademia Nazionale dei Lincei, Roma, Classe di Scienze Fisiche, Matematiche e Naturali. 2025, 36(1), S. 3-33. ISSN 1120-6330. eISSN 1720-0768. Verfügbar unter: doi: 10.4171/rlm/1063BibTex
@article{Lasiecka2025-10-20Uniqu-75331,
title={Unique continuation of static overdetermined magnetohydrodynamic equations},
year={2025},
doi={10.4171/rlm/1063},
number={1},
volume={36},
issn={1120-6330},
journal={Rendiconti Lincei. Matematica e Applicazioni},
pages={3--33},
author={Lasiecka, Irena and Priyasad, Buddhika and Triggiani, Roberto}
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