Lecture Notes On Regularity Theory For The Navierstokes Equations

 26,99 €

 26,99 €
Description de l’éditeur
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 2009–2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier–Stokes 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 Navier–Stokes equations.
The global unique solvability (wellposedness) of initial boundary value problems for the Navier–Stokes 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 wellposedness 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 Navier–Stokes equations. Together with introduction chapters, the lecture notes will be a selfcontained account on the topic from the very basic stuff to the stateofart in the field.
Contents:PreliminariesLinear Stationary ProblemNonLinear Stationary ProblemLinear NonStationary ProblemNonLinear NonStationary ProblemLocal Regularity Theory for NonStationary Navier–Stokes EquationsBehaviour of L3NormAppendix A: Backward Uniqueness and Unique ContinuationAppendix B: LemarieRiesset Local Energy Solutions
Readership: Undergraduate and graduate students in differential equtions and fluid mechanics.
Key Features:Unique treatment of certain topics