Geodesic
A solution class of the Euler equation in a torus with solenoidal velocity field. III
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 91-100

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We continue the study of the problem on the existence conditions for solenoidal solutions of the Euler equation in a torus $D$ with respect to a pair $(\mathbf{V},p)$ of vector and scalar fields such that the lines of the vector field $\mathbf{V}$ have a simple structure, coinciding with parallels and meridians of toroidal surfaces that are concentrically embedded in $D$. Here, in contrast to the previous two papers, the right-hand side of the Euler equation, i.e., the vector field $\mathbf{f}$ in $D$, is not given in a special form but is considered to be arbitrary.
Keywords: scalar and vector fields, curl.
Mots-clés : Euler equation, divergence 
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V. P. Vereshchagin; Yu. N. Subbotin; N. I. Chernykh. A solution class of the Euler equation in a torus with solenoidal velocity field. III. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 91-100. http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a10/