It is not yet known if the global attractor of the space-periodic 2D Navier-Stokes equations contains non-stationary solutions u(x,t) such that their energy and enstrophy per unit mass are constant ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Unless you’re a physicist or an engineer, there really isn’t ...

We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS). We prove that for an AC RDS the Ω-limit set $\Omega _{B}(\omega)$ of any bounded set B is nonempty, compact, ...

As we celebrate the International Year of Quantum Science and Technology (IYQ) in 2025, we look back on a century of quantum mechanics—a field that has fundamentally changed the way we understand ...

A huge mathematical breakthrough might have just been made, but a language barrier is slowing things down. New Scientist reports that Kazakh mathematician Mukhtarbay Otelbayev may have solved an ...

The axisymmetric Navier-Stokes equations describe the motion of incompressible fluids under the assumption of rotational symmetry around a fixed axis. This reduction in dimensional complexity retains ...

Jim Denier receives funding from the Australian Research Council. MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in ...

Erica Grace Cabanilla, my ERDT administrator, who took charge of all my stipends, reminded me gently that I am supposed to give my exit report on Jan. 26 as Visiting Researcher, although my ...