Volume 27, 2021
|Number of page(s)||24|
|Published online||06 December 2021|
Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct
School of Mathematical Sciences, Shanghai Jiao Tong University,
200240, P.R. China.
2 School of Mathematical Sciences, Center for Applied Mathematics, MOE-LSC, CMA-Shanghai and SHL-MAC, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China.
* Corresponding author: firstname.lastname@example.org
Accepted: 2 November 2021
This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where the controls are situated in both vertical walls. First, global exact controllability via boundary controls is established for a related Elsässer type system by applying the return method, introduced in Coron [Math. Control Signals Syst. 5 (1992) 295–312]. Similar results are then inferred for the original magnetohydrodynamics system with the help of a special pressure-like corrector in the induction equation. Overall, the main difficulties stem from the nonlinear coupling between the fluid velocity and the magnetic field in combination with the aim of exactly controlling the system. In order to overcome some of the obstacles, we introduce ad-hoc constructions, such as suitable initial data extensions outside of the physical part of the domain and a certain weighted space.
Mathematics Subject Classification: 93B05 / 76C99 / 93C20
Key words: Ideal incompressible magnetohydrodynamics / boundary control / global exact controllability
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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