Recent Progress in the Theory of the Euler and Navier–Stokes Equations London Mathematical Society Lecture Note Series

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.

Preface James C. Robinson, José L. Rodrigo, Witold Sadowski and Alejandro Vidal-López; 1. Classical solutions to the two-dimensional Euler equations and elliptic boundary value problems, an overview Hugo Beirão da Veiga; 2. Analyticity radii and the Navier–Stokes equations - recent results and applications Zachary Bradshaw, Zoran Grujić and Igor Kukavica; 3. On the motion of a pendulum with a cavity entirely filled with a viscous liquid Giovanni P. Galdi and Giusy Mazzone; 4. Modal dependency and nonlinear depletion in the three-dimensional Navier–Stokes equations John D. Gibbon; 5. Boussinesq equations with zero viscosity or zero diffusivity - a review Weiwei Hu, Igor Kukavica, Fei Wang and Mohammed Ziane; 6. Global regularity versus finite-time singularities - some paradigms on the effect of boundary conditions and certain perturbations Adam Larios and Edriss S. Titi; 7. Parabolic Morrey spaces and mild solutions of the Navier–Stokes equations - an interesting answer through a silly method to a stupid question Pierre Gilles Lemarié-Rieusset; 8. Well-posedness for the diffusive 3D Burgers equations with initial data in H1/2 Benjamin C. Pooley and James C. Robinson; 9. On the Fursikov approach to the moment problem for the three-dimensional Navier–Stokes equations James C. Robinson and Alejandro Vidal-López; 10. Some probabilistic topics in the Navier–Stokes equations Marco Romito.

James C. Robinson is Professor of Mathematics in the Mathematics Institute at the University of Warwick.
José L. Rodrigo is Associate Professor in the Mathematics Institute at the University of Warwick.
Witold Sadowski is Assistant Professor in the Institute of Applied Mathematics at the University of Warsaw.
Alejandro Vidal-López is a Lecturer in the Department of Mathematical Sciences at Xi'an Jiaotong-Liverpool University, China.