Abstract.
The long time existence of solutions to the Navier–Stokes equations in a cylinder and with boundary slip conditions is proved. The solutions are such that the azimuthal component of the velocity (swirl) is small in some neighbourhood of the axis of symmetry but it is large in some positive distance from it. To obtain this result the Leray–Schauder fixed point theorem is applied. The result can serve as the simplified mathematical description of the typhoon phenomenon.
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Communicated by K. Pileckas
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Zadrzyńska, E., Zaja̦czkowski, W.M. Global Regular Solutions with Large Swirl to the Navier–Stokes Equations in a Cylinder. J. math. fluid mech. 11, 126–169 (2009). https://doi.org/10.1007/s00021-007-0252-z
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DOI: https://doi.org/10.1007/s00021-007-0252-z