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 ...

We consider a hyperbolic singular perturbation of the incompressible Navier Stokes equations in two space dimensions. The approximating system under consideration arises as a diffusive reseated ...

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 ...

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge. Physics contains equations that ...

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 ...

Mathematics is awash with fiendish problems such as that of strong coupling, which crops up in physical systems from boiling water to superconductors where there are too many moving parts to be ...