Contemporary Mathematics. Fundamental DirectionsContemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направления2413-36392949-0618Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)32585ArticlesСтатьиResearch ArticleDissipation-induced instabilities in magnetized owsНарушения устойчивости намагниченных потоков, вызванные диссипациейKirillovO. N.КирилловО. Н.o.kirillov@hzdr.deHelmholtz-Zentrum Dresden Rossendorf1512201660VOL 60, NO (2016)ТОМ 60, № (2016)8210114112022Copyright ©; 2022, Contemporary Mathematics. Fundamental DirectionsCopyright ©; 2022, Современная математика. Фундаментальные направления2022Contemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направленияhttps://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/CMFD/article/view/32585We study local instabilities of a di erentially rotating viscous ow of electrically conducting incompressible uid subject to an external azimuthal magnetic eld. The hydrodynamically stable ow can be destabilized by the magnetic eld both in the ideal and in the viscous and resistive system giving rise to the azimuthal magnetorotational instability. A special solution to the equations of the ideal magnetohydrodynamics characterized by the constant total pressure, the uid velocity parallel to the direction of the magnetic eld, and by the magnetic and kinetic energies that are nite and equal - the Chandrasekhar equipartition solution - is marginally stable in the absence of viscosity and resistivity. Performing a local stability analysis we nd the conditions when the azimuthal magnetorotational instability can be interpreted as a dissipation-induced instability of the Chandrasekhar equipartition solution.Изучаются локальные нарушения устойчивости дифференциально вращающегося потока электропроводящей несжимаемой жидкости, находящейся под воздействием внешнего азимутального магнитного поля. Гидродинамически устойчивый поток может быть дестабилизирован магнитным полем как в случае идеальной системы, так и в случае системы с вязкостью и сопротивлением; при этом возникает азимутальная магнитовращательная неустойчивость. Специальное решение уравнений идеальной магнитогидродинамики, для которого полное давление постоянно, скорость жидкости параллельна направлению магнитного поля, а магнитная и кинетическая энергии конечны и равны друг другу (такое решение называется чандрасекаровской эквипартицией), маргинально устойчиво при отсутствии вязкости и сопротивления. 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