Approximation Methods for Navier-Stokes Problems: by C. J. Amick (auth.), Reimund Rautmann (eds.)

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

Example text

7-,)1 denotes or ~ o ~ | -~ ~3 some norm of the vector ~' we simply write and IV{I =tv I , o Proposition 4. ( then I~ mo=m /'K. or There holds the inequality A I{I . Similarly . 31 ~'-~--~/~; where ~ Z l , , B~_ Let ¢ A ~ Th~ constants Proposition ~. ~,=~z l ( ~ + z ) if ~ ~ ~ <2 the= depend on ~ ~ , Z-~ Lm(o~)) n L " ( ~ ) , ~ , . , ~x,~)[l¢i,+ l ~1,,]. where ~-I___~-I - I/8 . ~f z ~, ~ , ~ ~, then Consider the question concerning the smoothness of the function ~(¢) (~) ~ Let -~ ~ ( ~ - ~ ) - - 60 ~) be an arbitrary ve~ctor and let ~ C Y n ) .

The a n s w e r is if one c a n n o t after the p r e d i c t a b i l i t y time : if we a c t u a l l y p r o d u c e a long t e r m n u m e r i c a l s o l u t i o n r e p r o d u c i n g the o b s e r v e d s t a t i s t i c s of real flows, we shall have m a d e an i m p o r t a n t step in our c o m p r e h e n s i o n of the t u r b u l e n c e problem : such a m o d e l w i l l be an i m p o r t a n t v e r i f i c a t i o n theory. , as a c t u a l l y h a p p e n s of the atmosphere. easily Such m o d e l s sophisticated models interacts with various physical mechanisms like t o p o g r a p h y effect, port, heat transfers, water vapor in m o d e l s of the g e n e r a l statistics involved.

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. I6. I. A. Pearson, Expansions at small Reynolds num- bers for the flow past a sphere and a circular cylinder, J. Fluid Mech. I7. H. , 2, 237 (1957). The resistance to a particle of arbit- rary shape in translational motion at small Reynolds number, I8. I. Babenko, J. Fluid Mech. The perturbation a viscous 17, 561-595, theory of stationary flows of incompressible bers, Preprint (I963).

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