Abstract
A system of equations with respect to a pair (V, p) of a scalar field and a vector field in a torus D is considered. The system consists of the Euler equation with a given vector field f and the solenoidality equation for the field V. We seek for solutions (V, p) of this system such that the lines of the vector field V inside D coincide with meridians of tori embedded in D with the same circular axis. Conditions on the vector field f under which the problem is solvable are established, and the whole class of such solutions is described.
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Original Russian Text © V.P. Vereshchagin, Yu.N. Subbotin, N.I. Chernykh,, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 4.
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Vereshchagin, V.P., Subbotin, Y.N. & Chernykh, N.I. A solution class of the Euler equation in a torus with solenoidal velocity field. Proc. Steklov Inst. Math. 288 (Suppl 1), 211–221 (2015). https://doi.org/10.1134/S0081543815020224
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DOI: https://doi.org/10.1134/S0081543815020224