Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis
The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

Large eddy simulation (LES) is a method of scientific computation seeking to predict the
dynamics of organized structures in turbulent flows by approximating local, spatial averages …

Euler equations of incompressible fluids use and enrich many branches of mathematics,
from integrable systems to geometric analysis. They present important open physical and …

We consider the regularity criteria for the incompressible Navier–Stokes equations
connected with one velocity component. Based on the method from Cao and Titi (2008 …

Regularity criteria for the generalized viscous MHD equations Critères de régularité pour
les équations MHD généralisées Page 1 Ann. IH Poincaré – AN 24 (2007) 491–505 www.elsevier.com/locate/anihpc …

We improve the regularity criterion for the incompressible Navier–Stokes equations in the
full three-dimensional space involving the gradient of one velocity component. The method …

The question of spontaneous apparition of singularity in the 3D incompressible Euler
equations is one of the most important and challenging open problems in mathematical fluid …

We consider the initial–boundary value problem for the 3D Navier–Stokes equations. The
physical domain is a bounded open set with a smooth boundary on which we assume a …

In reference [13], by Constantin and Fefferman, a quite simple geometrical assumption on
the direction of the vorticity is shown to be sufficient to guarantee the regularity of the weak …