Partial Differential Equations in Fluid Mechanics

The Euler and Navier-Stokes equations are the fundamental mathematical models of fluid mechanics, and their study has greatly informed our understanding of the behaviour of complex fluids. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains surveys of recent progress and classical topics, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models, and several chapters address the Navier-Stokes equations directly, in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.