Click & drag on canvas to inject flow or draw solid boundary walls
Directly manipulate fluid velocity fields, inject vorticity pulses, test obstacle boundary friction, and numerically evaluate Clay Mathematics Institute smoothness bounds vs. finite-time singularity formation.
A classical theorem stating that a smooth solution of the 3D Euler/Navier-Stokes equations on $[0, T)$ breaks down at $T$ if and only if $\int_0^T ||\omega(\cdot, t)||_{L^\infty} dt = \infty$, where $\omega = \nabla \times u$ is vorticity.
Established that any potential space-time singularity of an incompressible Navier-Stokes flow must have 1-dimensional parabolic Hausdorff measure zero (partial regularity theorem).
The reported proof attempts to bound vortex stretching in $L^3$ space or construct an invariant manifold demonstrating global well-posedness, resolving the $1M Clay Millennium challenge.