Loitsiansky was correct in the infinite domain

Decaying isotropic, homogeneous, incompressible turbulence in a infinite domain is examined. The Saffman integral\footnote{P. G. Saffman, J. Fluid Mech. 27, 581 (1967).}: $\int_0^{\infty}r^2B_{ii}(r)dr$ is found to be zero not as previously assumed $\pi^2 M$. Under Saffman assumption the integral doesn't converge in the infinite domain. Using the same method on the Loitsiansky equation\footnote{L. G. Loitsiansky, Cent. Aero. Hydrodyn. Inst. Moscow, Report. No. 440 (Trans. NACA Tech. Memo. 1079), 1939.}: \begin{equation} \frac{\partial}{\partial t} \int^{\infty}_0 r^4 B_{LL}(r)dr = -2[B_{NN,L}(r) r^4]^{\infty}_0 + +2\nu[\frac{\partial B_{LL}(r)}{\partial r} r^4]^{\infty}_0 \end{equation} shows that for an infinite domain $\lim_{r \rightarrow \infty}r^4B_{NN,L}(r) = 0$. Contradicting the findings of I. Proudman \& W. H. Reid\footnote{I. Proudman and W. H. Reid, Philos. Trans. R. Soc. London Ser. A 247, 163 (1954).} and G. K. Batchelor \& I. Proudman\footnote{G. K. Batchelor and I. Proudman, Philos. Trans. R. Soc. London Ser. A 248, 369 (1956).}. However in a finite domain the above result found in this research do not hold.