Abstract
We study the Navier–Stokes equations of steady motion of a viscous incompressible fluid in \({\mathbb{R}^{3}}\). We prove that there are no nontrivial solution of these equations defined in the whole space \({\mathbb{R}^{3}}\) for axially symmetric case with no swirl (the Liouville theorem). Also we prove the conditional Liouville type theorem for axial symmetric solutions to the Euler system.
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Korobkov, M., Pileckas, K. & Russo, R. The Liouville Theorem for the Steady-State Navier–Stokes Problem for Axially Symmetric 3D Solutions in Absence of Swirl. J. Math. Fluid Mech. 17, 287–293 (2015). https://doi.org/10.1007/s00021-015-0202-0
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DOI: https://doi.org/10.1007/s00021-015-0202-0