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.
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Keywords: Ideal incompressible magnetohydrodynamics, boundary control, global exact controllability
@article{COCV_2021__27_1_A105_0,
author = {Rissel, Manuel and Wang, Ya-Guang},
title = {Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021099},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021099/}
}
TY - JOUR AU - Rissel, Manuel AU - Wang, Ya-Guang TI - Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021099/ DO - 10.1051/cocv/2021099 LA - en ID - COCV_2021__27_1_A105_0 ER -
%0 Journal Article %A Rissel, Manuel %A Wang, Ya-Guang %T Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021099/ %R 10.1051/cocv/2021099 %G en %F COCV_2021__27_1_A105_0
Rissel, Manuel; Wang, Ya-Guang. Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 103. doi: 10.1051/cocv/2021099
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