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"established theories" is a correct and usable phrase in written English.
You can use it whenever you want to refer to theories that have been widely accepted and are widely accepted as being true or valid. For example: "Economists agree that some of the most established theories of economic growth are the Solow Growth Model and the Endogenous Growth Model."
Exact(56)
If confirmed, the discovery challenges established theories about the formation of our planet.
It does this by situating piloting within established theories of policy formulation and implementation, and illustrating using an empirical case.
The practitioner acts in a way that is independent of established theories and techniques and constructs a new theory of the unique case.
Analysis of these intensity fluctuations enables the determination of the distribution of particle diffusion coefficients, which are converted into a size distribution using established theories.
The final purpose of this paper is therefore to iii) explore the relation between these constructs and whether established theories of acceptability explain variations within these constructs.
It further explore the relation between these constructs and whether established theories of acceptability explain variations within these constructs as well.
At a high filler loading (>2 wt%), the mechanical properties of composites do not fit established theories due to agglomeration of titanate nanostructures.
The paper applies the established theories of non-linear diffusion and flows driven by surface tension to the dynamical behavior of a miscible mixture.
Similar(3)
This poor understanding of science adversely affects the ability of individuals to make informed decisions about science-related issues, including well-established theories like the big bang, which is rejected by nearly two-thirds of Americans (National Science Foundation, 2014).
We have well-established theories which have passed many tests, so a result claiming new physics amounts to an extraordinary claim, demanding extraordinary evidence.
The focus on originality and accessibility – publications exploring new areas of research using new paradigms, and avoiding testing well-established theories – is the exact opposite of what science needs to be doing to solve the troubling replication crisis.
More suggestions(15)
established probabilities
implemented theories
established principles
established predictions
established discourses
established methods
established understandings
established factors
established notions
established perspectives
established doctrine
formalized theories
formation theories
determine theories
established theoretical
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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