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Oseen, C. W., Über die Stokessche Formel und über eine verwandte Aufgabe in der Hydrodynamik. II.pdf


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4

ARKIV FÖR MATEMATJK, ASTRONOM! 0. FYSIK.

8 'lt fLU 1 (Xo, Yo· Zo) =

ef<

UuX'

BD

7.

N:O

1.

+ U12 Y' + U13 Z') dw +

Q

+(!u{(u'u11

+

v'u 12

s
+lt

'

+ ... -u

11
u du
-dn

Yo• Zo) =

+ f< u'„p1 -7.t1nq)ds+

cos nxds

s

,
J[

s

8 'lt fL v' (xo'

+ w'u13 )

ef<

U21

11

X'+

J

-du' - . . . d s
dn
'

U22

Y'

+ U23 Z') dw +

f

u'" p 2 - u2, n q) d s +

Q

+(! u

f

0

u' u 21

+ v' u + w'
22

s

+ur

1.t 23 )

cos n x d s +

s

J[ ,

J

du 21
du'
d
u--+···-u
21 dn
dn- · · · s ,

s

8 n: µw' (x 0 , y 0, Z 0 ) = (!

j<u

31

X'

+ U 32 Y' + u 33 Z') dc11 +

Q

+euo} u' U 31

+ v' U 32 + w' U 33 )

cos nx ds +J(u'„ p 9 -

u 3 ,n q) ds +

s

8

J[

+ r-lt

,dua1

U --

dn

s

+ ••• -

du'
dn

'U 31 ~ -

···

]d 8

'

tJ- (-I) Jds+ft{[ -a (-1) -du' + · · ·-u, -d- a
+ ~u 0 U, niJx
, (-1) -·· ·Jds.
r
Ox r dn
dniJx r

s