LOCAL EXACT CONTROLLABILITY FOR THE PLANAR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS

被引：5

作者：

Tao, Qiang ^{[1
,2
]}

机构：

[1] Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Peoples R China

[2] Shenzhen Univ, Shenzhen Key Lab Adv Machine Learning & Applicat, Shenzhen 518060, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2018年 / 56卷 / 06期

基金：

美国国家科学基金会;

关键词：

compressible MHD equations; controllability; continuity dependence; NAVIER-STOKES SYSTEM; EXACT INTERNAL CONTROLLABILITY; NULL CONTROLLABILITY; EXISTENCE; RATES;

D O I：

10.1137/17M113407X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper is concerned with the boundary controllability for the planar compressible magnetohydrodynamic equations. For a constant target trajectory, we prove that the system is exactly controllable by the control functions acting on the whole boundary, given the small H-2 initial perturbation. The proof relies on the continuous dependence of the solution on the initial data and the Carleman inequality for the velocity and magnetic fields. A suitable space for the density is introduced in the fixed point argument to reduce the regularity of the initial data.

引用

页码：4461 / 4487

页数：27

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