It is well known that Leray's Inequality holds under stringent outflow condition (SOC). But Leray's Inequality does not hold under general outflow condition (GOC). This fact has been proved by Takeshita . But, Takeshita's argument is very complicated. The author succeeds in giving an alternative proof which is simpler than Takeshita's. Moreover, the result is an improvement of Takeshita's result.
"Takeshita's examples for Leray's Inequality." Hokkaido Math. J. 42 (1) 113 - 120, February 2013. https://doi.org/10.14492/hokmj/1362406641