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"widely exist in" is grammatically correct and can be used in written English.
It is typically used to describe something that is present or can be found in many different places or situations. Here is an example sentence: "Cultural stereotypes exist in many societies, but they are widely existent in more conservative regions."
Exact(59)
Taken together, these lines of evidence suggest that SEPs widely exist in the serum and might show wide individual differences.
Noises widely exist in interactive genetic algorithms.
In offshore environment, newly deposited quaternary loose sediments widely exist in the world.
The distributed production lines widely exist in modern supply chains and manufacturing systems.
Convection diffusion reaction processes widely exist in chemical engineering and other sectors of industry.
Multi-Input Multi-Output (MIMO) regression estimation problems widely exist in engineering fields.
Hierarchical helical structures widely exist in both artificial and biological materials.
Non-smooth sandwich systems with dead-zone widely exist in the real engineering applications.
Ni2Cr-type superlattices widely exist in Ni Cr based and Ni Mo based alloys.
Optimization problems widely exist in radar, mobile, and communication system designs.
Similar(1)
Ordered data widely exists in practical problems.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com