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Exact controllability for the magnetohydrodynamic equations
Author(s) -
Barbu Viorel,
Havârneanu Teodor,
Popa Cătălin,
Sritharan S. S.
Publication year - 2003
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.10072
Subject(s) - controllability , magnetohydrodynamic drive , mathematics , magnetohydrodynamics , mathematical analysis , steady state (chemistry) , physics , magnetic field , chemistry , quantum mechanics
We study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations. The main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough. We reduce the local exact controllability of the steady state solutions of the magnetohydrodynamic equations to the global exact controllability of the null solution of the linearized magnetohydrodynamic system via a fixed‐point argument. The treatment of the reduced problem relies on two Carleman‐type inequalities for the backward adjoint system. © 2003 Wiley Periodicals, Inc.