Recent Progress in the Theory of the Euler and Navier–Stokes Equations

James C. Robinson, José L. Rodrigo, Witold Sadowski, Alejandro Vidal-López

• Publisher: Cambridge University Press
• Year: 2016
• Print ISBN:
  9781107554979
• eBook ISBN:
  9781316590102
• Topic: Mathematics
• Subtopic: Differential Equations
• Index: Mathematics

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 Burgers equations, and probabilistic aspects of the Navier–Stokes equation. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Table of contents

• Cover
• Series information
• Title page
• Copyright information
• Dedication
• Table of contents
• Preface
• List of contributors
• 1 Classical solutions to the two-dimensionalEuler equations and elliptic boundary valueproblems, an overview
• 2 Analyticity radii and the Navier–Stokesequations: recent results and applications
• 3 On the motion of a pendulum with a cavityentirely filled with a viscous liquid
• 4 Modal dependency and nonlinear depletionin the three-dimensional Navier–Stokesequations
• 5 Boussinesq equations with zero viscosity orzero diffusivity: a review
• 6 Global regularity versus finite-timesingularities: some paradigms on the effect ofboundary conditions and certainperturbations
• 7 Parabolic Morrey spaces and mild solutionsof the Navier–Stokes equations. Aninteresting answer through a silly method toa stupid question
• 8 Well-posedness for the diffusive 3D Burgersequations with initial data in H[sup(1=2)]
• 9 On the Fursikov approach to the momentproblem for the three-dimensionalNavier–Stokes equations
• 10 Some probabilistic topics in theNavier–Stokes equations