I've seen a number of career/jobs questions on mathoverflow before, so I thought I would ask. Please excuse me if this isn't the best place for this specific question. Lately I've been really considering a job outside of academia after I finish my dissertation. The wealth of information out there, including from sites like this one, can be a bit hard to sift through. I've noticed that getting a math job outside of academia can be anywhere between certain and impossible depending on what you want to do. E.g. if you want to work on applied numerical analysis or applied statistics it's easy as pie, but if you want to find a non-academic job working on etale cohomology you'll be out of luck.
My question is where do PDEs fall in this spectrum? More precisely, what kind of jobs outside of academia are there where the theory of partial differential equations is an essential part of the job? Or are deriving the equations and throwing them into a computer for numerical simulation the only steps of interest in non-academic jobs?
Edit: In an effort to make the question more on topic for this site, what sorts of applications of variational methods, regularity theory, blowup analysis, etc can one expect to use in an industrial setting?
