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A rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier Stokes equations, this book provides self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn, and Nirenberg. Appendices provide background material and proofs of some 'standard results' that...

The rigorous mathematical theory of the Navier Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive...