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Full Description
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.
Contents
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.
