Local exact controllability to trajectories of the magneto-micropolar fluid equations

Anh, Cung The; Toi, Vu Manh

doi:10.3934/eect.2017019

Cited by 4 publications

(1 citation statement)

References 32 publications

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“…In Sec.3, we discuss the backward topological property of a pullback attractor in the original spaces E and E 0 . The concept of a pullback attractor we use here depends on the trajectory space and the translation operator, which is slightly different from the stand one defined by an evolution process (see [1,4,8,9,12,13,25]), or a multi-valued process (see [5,6,10,11,26,30]), but they have some connections.…”

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confidence: 99%

Backward controllability of pullback trajectory attractors with applications to multi-valued Jeffreys-Oldroyd equations

Li¹,

Wang²,

She³

2018

Evolution Equations &Amp; Control Theory

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This paper analyzes the time-dependence and backward controllability of pullback attractors for the trajectory space generated by a nonautonomous evolution equation without uniqueness. A pullback trajectory attractor is called backward controllable if the norm of its union over the past is controlled by a continuous function, and backward compact if it is backward controllable and pre-compact in the past on the underlying space. We then establish two existence theorems for such a backward compact trajectory attractor, which leads to the existence of a pullback attractor with the backward compactness and backward boundedness in two original phase spaces respectively. An essential criterion is the existence of an increasing, compact and absorbing brochette. Applying to the non-autonomous Jeffreys-Oldroyd equations with a backward controllable force, we obtain a backward compact trajectory attractor, and also a pullback attractor with backward compactness in the negative-exponent Sobolev space and backward boundedness in the Lebesgue space.2000 Mathematics Subject Classification. Primary: 35B40, 35B41; Secondary: 37B55.

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confidence: 99%

Backward controllability of pullback trajectory attractors with applications to multi-valued Jeffreys-Oldroyd equations

Li¹,

Wang²,

She³

2018

Evolution Equations &Amp; Control Theory

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Small-time global approximate controllability for incompressible MHD with coupled Navier slip boundary conditions

Rissel,

Wang

2024

Journal de Mathématiques Pures et Appliquées

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Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct

Rissel

Wang

2021

ESAIM: COCV

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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 J.M., Math. Control Signals Systems, 5(3) (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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Local exact controllability to trajectories of the magneto-micropolar fluid equations

Cited by 4 publications

References 32 publications

Backward controllability of pullback trajectory attractors with applications to multi-valued Jeffreys-Oldroyd equations

Backward controllability of pullback trajectory attractors with applications to multi-valued Jeffreys-Oldroyd equations

Small-time global approximate controllability for incompressible MHD with coupled Navier slip boundary conditions

Global exact controllability of ideal incompressible magnetohydrodynamic flows through a planar duct

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