I think many theoritical researchers do not care about practical applications (from physics university time, I even remember a disdain from some students about applications because it's "dirty", meaning badly approximated). In any case, it's hard to predict, but sometimes theoritical results have real world impact eventually. Crazy theories like quantum physics and Relativity are used to for computing (semiconductors and newer quantum computers) and GPS now.
Having this proven solution will probably motivate new research directions, and it could improve the understanding of this fluid mechanics equations, which has applications everywhere fluids are used...