"not many studies" is a perfectly correct and usable phrase in written English.
You can use it when you want to indicate that something is of limited quantity or frequency. For example, "Not many studies have been conducted on the effects of this new drug."
Unfortunately, not many studies analyze the aspects of LR regulations that might be critical in practice.
In spite of this, there are not many studies assessing irrigation water management of landscapes.
Currently, there are not many studies about the body of knowledge on research-based learning in Thailand.
Not many studies are currently found that include the presence of an aqueous aggressive environment, a major concern when referring to the marine structures.
With current development in the pedagogy of teaching and learning approaches in the world, not many studies have been done on outdoor learning in Malaysia.
Works in literature are mostly focused on external implementation of cryogenic; thereby not many studies are concerned in its internal application (i.e. through-tool).
There were not many studies focused on the application of blog technology to the professional development of nursing education in Taiwan.
However, not many studies address the impact of such margins in arable landscapes on the abundance of macro-invertebrates in arable fields.
Despite that, not many studies have considered using empirical data to investigate what features of the road environment influence a driver's compliance choice.
Despite the common use of Thimerosal as a preservative in childhood vaccines since the 1930s, there are not many studies on ethylmercury toxicokinetics and toxicodynamics in infants.
Although the body of longitudinal studies describing changes has expanded in the past decade, not many studies have documented influences on the changing pragmatic systems.
