Exact boundary controllability for the ideal magneto-hydrodynamic equations

被引：5

作者：

Kukavica, Igor ^{[1
]}

Novack, Matthew ^{[2
]}

Vicol, Vlad ^{[3
]}

机构：

[1] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA

[2] Inst Adv Study, Sch Math, 1 Einstein Dr, Princeton, NJ 08540 USA

[3] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 318卷

关键词：

D O I：

10.1016/j.jde.2022.02.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We address the problem of controllability of the MHD system in a rectangular domain with a control prescribed on the side boundary. We identify a necessary and sufficient condition on the data to be null-controllable, i.e., can be driven to the zero state. We also show that the validity of this condition allows the states to be stirred to each other. If the condition is not satisfied, one can move from one state to another with the help of a simple shear external magnetic force. (C)& nbsp;2022 Elsevier Inc. All rights reserved.

引用

页码：94 / 112

页数：19

共 50 条

[31] APPLICATION OF LAPLACE TRANSFORM TO SOLUTION OF BOUNDARY LAYER EQUATIONS .2. MAGNETO-HYDRODYNAMIC BLASIUS PROBLEM [J].

APELBLAT, A .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1968, 25 (03) :888-&

[32] Regularity criteria for suitable weak solutions to the four dimensional incompressible magneto-hydrodynamic equations near boundary [J].

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[33] MAGNETO-HYDRODYNAMIC WAVES IN THE IONOSPHERE [J].

AKASOFU, SI .

JOURNAL OF ATMOSPHERIC AND TERRESTRIAL PHYSICS, 1959, 15 (1-2) :156-160

[34] MAGNETO-HYDRODYNAMIC WAVES AND SUNSPOTS [J].

ALFVEN, H .

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 1945, 105 (01) :3-16

[35] MAGNETO-HYDRODYNAMIC WAVES IN A PLASMA [J].

ASTROM, E .

NATURE, 1950, 165 (4208) :1019-1020

[36] MAGNETO-HYDRODYNAMIC THRUST BEARING [J].

KAPUR, VK .

BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES TECHNIQUES, 1968, 16 (05) :427-&

[37] MAGNETO-HYDRODYNAMIC POWER GENERATION [J].

EULER, KJ .

ATOM & STROM, 1971, 17 (7-9) :137-+

[38] LONGITUDINAL MAGNETO-HYDRODYNAMIC WAVES [J].

ANDERSON, NS .

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 1953, 25 (03) :529-532

[39] NOTES ON MAGNETO-HYDRODYNAMIC EQUILIBRIUM [J].

HAMADA, S .

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[40] MAGNETO-HYDRODYNAMIC SHOCK WAVES [J].

HELFER, HL .

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