### Golovin S.V.

## Non-stationary flows of electrically conducting liquid with constant total pressure

The talk is devoted to the description of ideal MHD flows, in which the total pressure is constant in the whole area occupied by the flow. To this end we make use of a special curvilinear system of coordinates, where magnetic lines and particle trajectories serve as two families of coordinate curves in (1+3)D space. Flows with constant total pressure are described by the overdetermined system of PDEs involving a vector wave equation and a nonlinear incompressibility condition. Integration of this system and construction of solutions requires separation of variables in a certain scalar nonlinear equation and consequent integration of overdetermined systems of PDEs. We give examples of explicit exact solutions that possess functional arbitrariness and describe flows with nontrivial topology of magnetic tubes.

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