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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
12.7. Stokes Equations for Viscous Incompressible Fluids 1079
In the problem on the motion of a bounded body at a constant velocity a in an immov-
able fluid, the initial condition (3) is supplemented with the boundary conditions
u|
xS
= a, u|
|x|→∞
0. (6)
We point out that no conditions on the pressure p are needed in the above-stated prob-
lems for the Stokes equations.
Stokes equations in the rectangular Cartesian coordinates.
In the rectangular Cartesian coordinates (x, y, z), the Stokes equations (1)–(2) have the
form
∂u
1
∂t
=
∂p
∂x
+ ν
2
u
1
∂x
2
+
2
u
1
∂y
2
+
2
u
1
∂z
2
+ f
1
,
∂u
2
∂t
=
∂p
∂y
+ ν
2
u
2
∂x
2
+
2
u
2
∂y
2
+
2
u
2
∂z
2
+ f
2
,
∂u
3
∂t
=
∂p
∂z
+ ν
2
u
3
∂x
2
+
2
u
3
∂y
2
+
2
u
3
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Publisher Resources

ISBN: 9781466581494