Geodesic
Axisymmetric incompressible flows with bounded vorticity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 3, pp. 475-496

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This paper is devoted to the proof of global existence and uniqueness results for the three-dimensional incompressible Euler equations with a particular geometrical structure. The focus is on so-called axisymmetric solutions without swirl and on helicoidal solutions. The aim is to prescribe regularity conditions on the vorticity as close as possible to those formulated in the two-dimensional setting by V. I. Yudovich. 
@article{RM_2007_62_3_a3,
     author = {R. Danchin},
     title = {Axisymmetric incompressible flows with bounded vorticity},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {475--496},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2007_62_3_a3/}
}
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R. Danchin. Axisymmetric incompressible flows with bounded vorticity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 3, pp. 475-496. http://geodesic.mathdoc.fr/item/RM_2007_62_3_a3/