Navier-Stokes regularity problem

Type: Concept

As of November 2026, Navier-Stokes regularity problem has not yet been heard in an analyzed podcast episode.

The question of whether the Navier–Stokes equations always have smooth solutions in three-dimensional Euclidean space, given some initial conditions and possibly an external force, has been a longstanding unsolved problem in mathematics since the early 20th century. The equations are a system of partial differential equations that describe the motion of a fluid in space. Although computational solutions to the Navier–Stokes equations are used in a large number of practical applications, there is