%0 Journal Article
%A Doering, Charles R.
%T The 3D Navier-Stokes Problem
%D 2009
%J Annual Review of Fluid Mechanics,
%V 41
%N Volume 41, 2009
%P 109-128
%@ 1545-4479
%R https://doi.org/10.1146/annurev.fluid.010908.165218
%K turbulence
%K initial value problem
%K incompressible Newtonian fluid mechanics
%K uniqueness of solutions
%K vortex stretching
%K regularity of solutions
%I Annual Reviews,
%X It is not known whether the three-dimensional (3D) incompressible Navier-Stokes equations possess unique smooth (continuously differentiable) solutions at high Reynolds numbers. This problem is quite important for basic science, practical applications, and numerical computations. This review presents a selective survey of the current state of the mathematical theory, focusing on the technical source of difficulties encountered with the construction of smooth solutions. It also highlights physical phenomena behind the mathematical challenges.
%U https://www.annualreviews.org/content/journals/10.1146/annurev.fluid.010908.165218