Like the post above, it sort of depends. If it's a physical process that you think you understand, then you're fine. If you're trying to mix random predictors that just happen to be correlated but one doesn't really affect the dependent variable, then you can get funky results.
Generally speaking, normal statistical tests like independent predictors...which is probably why you're asking the question. However, as a whole, your regression model should not be less accurate or have poorer prediction capable because of the correlation.
You're probably fine. My go-to first try would be a quadratic regression including linear interactions.
Also, look up multicollinearity. The wikipedia page will probably reassure you.