Boundary Integral and Singularity Methods for Linearized Viscous Flow
C. Pozrikidis
Cambridge University Press, 1992
H= - 1/(2pl^{2}) [ ln r + ker_{0}(|l|r) - (i kei_{0}(|l|r)] (12)
Substituting further (12) into (2.2.4), and carrying out the differentations we find the Green's function
G_{ij}(x, x_{0}) = d_{ij} A(R) + (^x_{i}^x_{j})/r^{2} B (R) - i 2/|l|^{2} (d_{ij}/r^{2} - 2 (^x_{i}^x_{j})/r^{4})
where R=|l|r,
and the functions A and B are defined as follows
A(x) = 2 [ ker_{0} (x) - kei'_{0}(x) / x] - 2 i [ kei _{0}(x)
- ker'_{0}(x) / x]
(15)
B(x) = 2 [ - ker_{0} (x) + 2 kei'_{0 }(x) / x] + 2 i [
kei_{0}(x) + 2 ker'_{0} (x) / x]
(16)
The pressure vector
is given by (2.6.19).