Up-to-Date Coverage of the NavierStokes Equation from an Expert in Harmonic Analysis

The complete resolution of the NavierStokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The NavierStokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics.

The book focuses on incompressible deterministic NavierStokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.

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