Despite much effort, the question of whether the Navier–Stokes equations allow solutions that develop singularities in finite time remains unresolved. Terence Tao discusses the problem, and possible routes to a solution.
Fluid dynamics is a mainstay of classical physics, but it also plays a role in fields such as biology, engineering and climate change. Solving problems in fluid dynamics often requires mathematical and computational ingenuity. This Collection showcases review and opinion pieces on fluid dynamics, especially at interfaces with other subjects.
Insects have mastered flight to a degree that scientists are only now starting to comprehend. Itai Cohen and colleagues discuss some of the outstanding challenges and opportunities for studying this fascinating and beautiful behaviour.
The fluid mechanics of active materials, built around the idea of living systems as condensed matter made of free-energy-consuming particles, gives insight into biology and opens new directions in physics. Sriram Ramaswamy discusses the history and future of the field.
Although the differential equations that describe the physical climate system are deterministic, there are reasons, both theoretical and practical, why computational representations of these equations should be stochastic. This Perspective surveys the benefits of stochastic modelling of weather and climate.
This year marks the 200th anniversary of the birth of George Gabriel Stokes, a physicist and mathematician best known for his contributions to fluid dynamics, but whose work was broader than that.