Partial Differential Equations in Fluid Mechanics

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.

• 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.