Lecture Notes On Regularity Theory For The Navier-Stokes Equations - Hardcover

Inhaltsangabe

The lecture notes in this book are based on the Tcc (Taught Course Centre for graduates) course given by the author in Trinity Terms of 20092011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the NavierStokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical Pde's theory in the style that is quite typical for St Petersburg's mathematical school of the NavierStokes equations. The global unique solvability (well-posedness) of initial boundary value problems for the NavierStokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the NavierStokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.

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