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"well established in" is correct and can be used in written English.
It is typically used to describe when something is widely known or accepted. For example: "The university is well established in the field of research and development."
Exact(51)
I'm now well established in my career.
The business is well established in Australia.
But by then he was well established in Europe.
Of these, five have become well established in the East.
This correlation is well established in the scientific literature.
I think this is now well established in psychology.
Similar(8)
He is 49 and well-established in real estate sales.
Bluetongue virus is currently well-established in France, where there is a shortage of vaccine.
The precautionary principle is well-established in medicine.
The use of ultrasonics is well-established in concrete diagnostics.
The healthcare system is well-established in the Kingdom; all Saudi nationals receive free health insurance.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com