Charles L. Fefferman is the Herbert Jones Professor in the Mathematics Department at Princeton University, New Jersey. He was awarded the Fields Medal in 1978. James C. Robinson is a Professor of Mathematics at the University of Warwick. He is also a Royal Society University Research Fellow and an EPSRC Leadership Fellow. José L. Rodrigo is a Professor of Mathematics at the University of Warwick, and has been awarded an ERC Consolidator Grant.

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• Preface Charles L. Fefferman, James C. Robinson and José L. Rodrigo; 1. Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier–Stokes equations Claude Bardos; 2. Time-periodic flow of a viscous liquid past a body Giovanni P. Galdi and Mads Kyed; 3. The Rayleigh–Taylor instability in buoyancy-driven variable density turbulence John D. Gibbon, Pooja Rao and Colm-Cille P. Caulfield; 4. On localization and quantitative uniqueness for elliptic partial differential equations Guher Camliyurt, Igor Kukavica and Fei Wang; 5. Quasi-invariance for the Navier–Stokes equations Koji Ohkitani; 6. Leray's fundamental work on the Navier–Stokes equations: a modern review of 'Sur le mouvement d'un liquide visqueux emplissant l'espace' Wojciech S. Ożański and Benjamin C. Pooley; 7. Stable mild Navier–Stokes solutions by iteration of linear singular Volterra integral equations Reimund Rautmann; 8. Energy conservation in the 3D Euler equations on T2 x R+ James C. Robinson, José L. Rodrigo and Jack W. D. Skipper; 9. Regularity of Navier–Stokes flows with bounds for the velocity gradient along streamlines and an effective pressure Chuong V. Tran and Xinwei Yu; 10. A direct approach to Gevrey regularity on the half-space Igor Kukavica and Vlad Vicol; 11. Weak-strong uniqueness in fluid dynamics Emil Wiedemann.