Annals of Mathematics, SECOND SERIES, Vol. 181, No. 2 (March, 2015), pp. 769-807 (39 pages) We study the nonhomogeneous boundary value problem for the Navier-Stokes equations of steady motion of a ...

SIAM Journal on Applied Mathematics, Vol. 35, No. 1 (Jul., 1978), pp. 97-116 (20 pages) The development of velocity profiles in the inlet region of channels or pipes is a classic problem of laminar ...

The study of free boundary problems in the Navier-Stokes equations addresses the subtle interplay between the dynamics of viscous, incompressible fluids and the evolution of interfaces whose locations ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Ms Tech | Science Photo Library via AP Unless you’re a physicist ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the ...

When the greatest mathematician alive unveils a vision for the next century of research, the math world takes note. That’s exactly what happened in 1900 at the International Congress of Mathematicians ...

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...