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The phrase "despite this pressure" is correct and usable in written English.
You can use it to indicate that something occurs or is true regardless of the pressure or challenges faced.
Example: "Despite this pressure, she managed to complete the project ahead of schedule."
Alternatives: "in spite of this pressure" or "regardless of this pressure".
Exact(5)
They are continuing, despite this pressure.
Despite this pressure and uncertainty, there are now at least four major independent film festivals around the country and at least two theaters, both small, dedicated to showing Chinese independent films.
Yet despite this pressure to specialize and differentiate, some of the extinct subfossil lemurs, such as Archaeolemur, may have had island-wide distributions during the Holocene, unlike the living lemurs.
Despite this, pressure to introduce rapid diagnostic tests has been strong.
Despite this pressure, most Chechen refugees are loath to return to Chechnya, where conditions are very dangerous, housing is almost nonexistent, and services have broken down.
Similar(53)
Yet despite all this pressure, there are Brazilian women moving in a different direction, such as Darcy Toledo, 42, and Jane Walter, 36, the founders of a photography business called the Nude Agency.
Despite all this pressure on the government's collective sense of ethics, the new Immigration Minister Peter Dutton continues to take a hard-line.
Despite all this pressure, university management refused to budge, and in April imposed a new five-year contract with industrial group Bouygues, who quickly rescinded many of the promises SOAS had made to the cleaners.
However, in the porcine circulatory system, a human-like disease distribution in the brachial and femoral arteries has been reported despite the absence of this pressure gradient [ 3- 6, 10].
For example, the shallow-water shrimp Palaemonetes varians tolerates pressures equivalent to 1000 m depth for at least a month and retains the ability to feed and successfully moult at this pressure, despite naturally inhabiting depths of less than 10 m (Cottin et al., 2012).
Despite this increased pressure on Libya's elite forces, Admiral Gortney insisted that the military was not going beyond the mandate of the United Nations resolution.
More suggestions(15)
despite this weakness
despite this benefit
despite this variation
despite this requirement
despite this attention
despite this concern
despite this shift
despite this report
despite this effort
despite this work
despite this demand
despite this result
despite this knowledge
despite this lack
despite this information
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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