Unsolved Problems
Showing 1-8 of 8 problems
Category
Problem Set
Status
Navier–Stokes Existence and Smoothness
Prove or give a counterexample: Do solutions to the Navier–Stokes equations in three dimensions always exist and remain smooth for all time?...
The Regularity Problem for Euler Equations
Do solutions to the 3D Euler equations for incompressible fluid flow remain smooth for all time, given smooth initial data?...
21st Century Fluids
Extend classical fluid dynamics to handle complex substances like foams, suspensions, gels, and liquid crystals....
Navier-Stokes Regularity
Do smooth initial data for 3D Navier-Stokes equations yield smooth solutions for all time?...
MLC Conjecture
Is the Mandelbrot set locally connected?...
Weinstein Conjecture
Does every regular compact contact-type level set carry a periodic orbit?...
Birkhoff Conjecture
If a billiard table is strictly convex and integrable, must its boundary be an ellipse?...
Navier-Stokes Existence and Smoothness
Do smooth solutions to Navier-Stokes equations exist globally in 3D? Or do finite-time singularities occur?...