Arnold's third problem

Arnold's third problem asks whether, for certain types of geometric objects called domains in three-dimensional space, a specific kind of flow known as steady, incompressible fluid flow can have infinitely many different solutions. In simpler terms, it questions if, under certain boundary conditions, there could be multiple ways a fluid might move smoothly through the same space, satisfying the physical laws of motion and mass conservation. This problem explores the uniqueness or multiplicity of these flows, contributing to our understanding of fluid behavior in complex geometries—a fundamental issue in mathematical physics.