Abstract: The Navier-Stokes equation on the Euclidean space ℝ3 can be expressed in the form ∂tu = Δu + B(u, u), where B is a certain bilinear operator on divergence-free vector fields u obeying the ...

Tomás Caraballo, José Real, Takeshi Taniguchi, On the Existence and Uniqueness of Solutions to Stochastic Three-Dimensional Lagrangian Averaged Navier-Stokes Equations, Proceedings: Mathematical, ...

In contrast, the Navier-Stokes equations incorporate viscous effects and are instrumental in describing real-world turbulent flows, boundary layer phenomena, and energy dissipation.

The Navier-Stokes equations have wide application, to aircraft, train and car design, air pollution analysis, ocean currents and weather prediction. Stokes is honoured by a commemorative plaque in ...

By Andy Kiersz Jan 23, 2014, 3:10 PM PT The Navier-Stokes equations describe how water flows in turbulent situations. williams_jt / Flickr ...