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

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.

• 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.