Conditions of nonlinear stability of plane and helical magnetohydrodynamic flows

V. A. Vladimirov*, Yu G. Gubarev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The stability problem of stationary flows of density-homogeneous ideal incompressible liquid in magnetic field is studied. Only such the magnetohydrodynamic flows are considered that have one of the symmetry types, translational, axial, rotational, helical. Sufficient conditions are obtained for nonlinear stability of the studied flows in regard to disturbances of the same symmetry. Proofs of these conditions are carried out by the method of motion integral connective based on construction of functionals with absolute minima at given stationary solutions. Every functional is a sum of kinetic energy, integral of arbitrary function of Lagrangian coordinate and some other integral characteristic of the studied flows.

Original languageEnglish
Pages (from-to)442-450
Number of pages9
JournalPrikladnaya Matematika i Mekhanika
Issue number3
Publication statusPublished - May 1995

ASJC Scopus subject areas

  • Applied Mathematics


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