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A nonexistence result for axially symmetric flows with constant angular velocities at infinity

  • Alan R. Elcrat (a1) and David Siegel (a2)

Synopsis

If von Kármán's substitution is made in the Navier-Stokes equations, and boundary conditions corresponding to a flow in all of space with constant angular velocities at infinity are imposed, a boundary value problem analgous to those for flow above a rotating disk and between rotating disks is obtained. It is shown here that this problem has no solution.

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1von Kármán, T.. Über laminare und turbulente Reibung. Z. Angew.Math. Mech. 1 (1921), 233252.
2Batchelor, G. K.. Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow. Quart. J. Mech. Appl. Math. 4 (1951), 2941.
3McLeod, J. B.. The existence of axially symmetric flow above a rotating disk. Proc. Roy. Soc. London Ser. A 324 (1971), 391414.
4Hartman, P.. The swirling flow in boundary layer theory. Arch. Rational Mech. Anal. 42 (1971), 137156.

A nonexistence result for axially symmetric flows with constant angular velocities at infinity

  • Alan R. Elcrat (a1) and David Siegel (a2)

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