The phrase "do not exist beyond" is grammatically correct and can be used in written English.
It means that something does not continue or is not present outside of a certain limit or boundary. Example: The company's operations do not exist beyond the local market. (meaning the company's operations only exist within the local market and not outside of it).
As usual for this type of blow-up result similar in spirit to the classical Keller-Segel model for chemotaxis [26, 27], the proof only ensures that solutions for those initial data do not exist beyond a finite maximal time of existence.
In other words, spirals do not exist beyond ∂ R ∞.
Spelman provides a safe space where these caricatures of African American womanhood simply do not exist beyond a classroom lecture or textbook.
As clear retirement guidelines in psychiatry do not exist, beyond the need to maintain competence [ 6], psychiatrists may choose to keep working well into old age.
Either that or photographs of fake-women, who don't exist beyond their beguiling "sexually available" pixels.
Although the figures Fréger photographs are drawn from real Japanese custom, he refers to "YOKAINOSHIMA" (meaning "island of the Yokai") as an invention, a place inhabited by monsters "that does not exist beyond the photographer's imagination".
Despite its widespread use, a formal definition of the language did not exist beyond Daylight's SMILES Theory Manual and tutorials.
The longest lasting lineage survived for more than 180 million years, whereas the shortest did not exist beyond a few million years.
For so long, in a society where patriarchy reigned supreme, women did not exist beyond the parameters define by their husbands, male friends, bosses, or male-centered society.
The other informant stated that political will does not exist beyond rhetoric speeches and formal regulations.
On the other hand, intensive care in underdeveloped countries often does not exist beyond the recovery room.
