Sinai’s Dynamical System Perspective on Mathematical Fluid Dynamics

We review some of the most remarkable results obtained by Ya.G. Sinai and collaborators on the difficult problems arising in the theory of the Navier–Stokes equations and related models. The survey is not exhaustive, and it omits important results, such as those related to “Burgers turbulence”. Our main focus in on acquainting the reader with the application of the powerful methods of dynamical systems and statistical mechanics to this field, which is the main original feature of Sinai’s contribution.

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