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By C. J. Amick (auth.), Reimund Rautmann (eds.)

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Extra info for Approximation Methods for Navier-Stokes Problems: Proceedings of the Symposium Held by the International Union of Theoretical and Applied Mechanics (IUTAM) at the University of Paderborn, Germany, September 9 – 15, 1979

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633-654. solutions in two dimensions, 20 (I965), 341-372. I3. R. R. Smith, On the linearized hydrodynamical ons in two dimensions, (I967), I4. I. Babenko, equati- Arch. Rational Mech. Anal. 25 behavior of the vorticity at 1-25. On the asymptotic large distance from a body in the pla~e flow of a viscous fluid, Prikl. Math. Mech. I5. D. F. Weinberger, Asymptotic solutio~ of the stationary Stokes equations, 34 (I970), properties two-dimensional 9II-925. of Leray's Navier- Uspehi Math. Nauk Tom XXIX, 2 (1974) I09-I229.

Suppose we have a stationary solutio~ in ~ B finite Dirichlet integral and satisfying the condition ~ a ~ -~-~o~,~+0 F ~ O at infinity. Then , then ~i(~)~--- " ~ O 0 "/,,L{'3C,)="~ + 0C~-'I~ is any arbitrarily small quantity. Since fact established by R. Finn [8] with ~dC~) ~ . 2) is established under assum- the question whether the solution of equation integral and what are these minimal conditions on the solution in the whole of the space that ~X~--~ (0°I) 0 for differs from zero is still open.

CR,~ ) dC~ 7 ) in ~0~~o)X 18 The rest of the properties of the Green's matrix will be given below in case of need. 2. I) are reasonable from physical stand- point as well. I) there holds the relation "lX,c x ~ - "u~ = 0 (2o2) (l=l-~) , was proved by the autkor in I972 [7~ • Earlier R. 3) was sufficient to obtain the asymptotics of the difference u . 4) is the vector force exerted by the flow on the body. 4) that wake region in the direc- , and that the decay of the difference inside it is the slowest.

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