[davnn]

> This is an important question in the theory of nonlinear partial differential equations, but is probably not as relevant to real fluid flow as a lay reader might imagine.

What kinds of problems does it solve to know an answer to this question? Honestly curious, please do not take this as offensive/dismissive.

[wwalker3]

If mathematicians could solve these kinds of problems, they could answer valuable questions like "Will this equation always have a physically meaningful solution?" If the answer was "No", then we would know that the equation can't be a faithful model of reality.

We already know that the incompressible Euler equations can't be a faithful model, for reasons I've mentioned elsewhere in the thread. But I think the hope is that if they can answer these questions for incompressible Euler, then they can eventually extend their techniques to more complex fluid equations like Navier-Stokes, which people generally assume (but can't yet prove) is physically reasonable.

Simulation has great practical value, but it doesn't give you any guarantees about the behavior of the solutions for all the cases you haven't actually tried.