If what you mean by "general solution for Navier-Stokes" is something like the Millennium Prize problem (proving general existence & uniqueness of solutions for

If what you mean by "general solution for Navier-Stokes" is something like the Millennium Prize problem (proving general existence & uniqueness of solutions for NS), then no, at least not as far as I can see. This work is about a different problem than NS: they are mainly interested in the advection of passive tracers, e.g., a blob of ink, in a chaotically-evolving fluid field. To do this, they assume a number of things: their fluid equations are subjected to stochastic forcing, which makes available a bigger bag of mathematical tools than deterministic chaotic systems (like high Reynolds number NS without stochastic forcing). They also assume periodic boundary conditions, which enables explicit calculations using Fourier series representations. (Physical boundaries play an important role in many kinds of turbulent flows but make the mathematical analysis harder.) And, in 3d, a hyperviscosity term (4th derivatives in space instead of the usual 2nd derivatives associated with viscosity), which makes solutions more smooth. That being said, proving new theorems in this area is hard. I think it's very nice work.