Turbulence and the statistical theory of nonlinear dynamics
Is there a general theory that predicts the statistical behavior of turbulent fluid flow directly from the Navier-Stokes equations, and can fully chaotic dynamical systems be understood from first principles?
History and references
Still open in the literature as of 2026.
Ginzburg's problem #11 covered nonlinear physics broadly: turbulence, solitons, chaos, and strange attractors. Solitons and low-dimensional chaos (the universal Feigenbaum route to chaos) are comparatively well understood mathematically, but fully developed turbulence still lacks a first-principles statistical theory that closes the energy cascade beyond Kolmogorov's 1941 phenomenological scaling. The closely related Navier-Stokes existence-and-smoothness question remains an unsolved Clay Mathematics Institute Millennium Prize Problem as of 2026.
Turbulence is everywhere, from a stirred coffee cup to interstellar gas, and nobody has ever derived from first principles why it looks the way it does.
References
- What problems of physics and astrophysics seem now to be especially important and interesting (thirty years later, already on the verge of the XXI century)?, V L Ginzburg, Physics-Uspekhi 42 (4) 353-373, 1999
- Navier-Stokes Existence and Smoothness, Clay Mathematics Institute, Millennium Prize Problems, 2000
Solutions 0
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