Invariant hyperplanes for 2D Navier–Stokes equations perturbed by nonlocal terms
Abstract We study the Navier-Stokes equations on the two-dimensional torus $$\mathbb {T}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> with a single input bilinear control term which forces the evolution to preserve hyperplanes. We reduce the problem to the solution of the Navier-Stokes system perturbed by a certain nonlinear nonlocal term and show the well-posedness of the initial value problem for such a system.
Authors
- Hélène Frankowska (ORCID: https://orcid.org/0000-0001-6237-4137)
- Piermarco Cannarsa (ORCID: https://orcid.org/0000-0003-2576-2004)
Institutions
- University of Rome Tor Vergata (IT)
- Centre National de la Recherche Scientifique (FR)
- Institut de Mathématiques de Jussieu-Paris Rive Gauche (FR)
- Sorbonne Université (FR)
Publication Details
- Journal
- Nonlinear Differential Equations and Applications NoDEA
- Published
- 2025-05-22
- DOI
- https://doi.org/10.1007/s00030-025-01070-6
- Primary Topic
- Stability and Controllability of Differential Equations
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Università degli Studi di Roma Tor Vergata
- Ministero dell'Università e della Ricerca