### Abstract

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 language | English |
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Pages (from-to) | 442-450 |

Number of pages | 9 |

Journal | Prikladnaya Matematika i Mekhanika |

Volume | 59 |

Issue number | 3 |

Publication status | Published - May 1995 |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Prikladnaya Matematika i Mekhanika*,

*59*(3), 442-450.

**Conditions of nonlinear stability of plane and helical magnetohydrodynamic flows.** / Vladimirov, V. A.; Gubarev, Yu G.

Research output: Contribution to journal › Article

*Prikladnaya Matematika i Mekhanika*, vol. 59, no. 3, pp. 442-450.

}

TY - JOUR

T1 - Conditions of nonlinear stability of plane and helical magnetohydrodynamic flows

AU - Vladimirov, V. A.

AU - Gubarev, Yu G.

PY - 1995/5

Y1 - 1995/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0029296503&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029296503&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0029296503

VL - 59

SP - 442

EP - 450

JO - Prikladnaya Matamatika i Mekhanika

JF - Prikladnaya Matamatika i Mekhanika

SN - 0032-8235

IS - 3

ER -