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On general axisymmetric explicit solutions for the Navier-Stokes equations. (English) Zbl 1291.35186
Summary: We present some new results on general axisymmetric explicit solutions for Navier-Stokes equations. We give the formulas for the solutions and prove, depending on the data, to what space the solutions belong to. By the uniqueness theorem of Ladyzhenskaya-Lions-Prodi, our formulas show that if the force and the initial velocity are symmetric then the solution will stay symmetric forever.
MSC:
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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