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Is there any way a pure math guy can get his rigorous math fix while simultaneously moving fusion research forward? Is fusion simply too complicated to take a pure math approach? What open math questions are there pertaining to fusion?

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The issue is that pure math has its own set of internal gauges for progress, and progress would mean that you have found a general proof technique which allows you to get good inequalities on the behavior of certain equations. The rigorous results usually necessarily follow a long period of heuristic piddling around, where all the properties are first established with scientific standards of certainty, then later made rigorous (with the occasional surprise, of course). If you are looking for a math problem, this is different from looking for a math problem with practical application. – Ron Maimon Feb 16 '12 at 8:10

There's a lot of research being done in computational magnetohydrodynamics. This is the study of the flow of ionic fluids, usually in confined magnetic fields. The governing equations of magnetohydrodynamics are a coupling of both the Navier-Stokes equations and Maxwell's equations of electromagnetism. In pure/applied mathematics there is the famous problem of smoothness in solutions to the Navier-Stokes equations.

Most of the problems in fusion energy are mostly engineering problems but there is still a lot of theoretical work being done.

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But the issue is that any of the rigorous results will almost certainly not be of any practical help to anyone trying to understand the qualitative or quantitative phenomena in these equations, because the rigorous difficulties are elsewhere than the physical difficulties. – Ron Maimon Feb 16 '12 at 8:08

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