This paper surveys various precise (long-time) asymptotic results for the solutions of the
Navier-Stokes equations with potential forces in bounded domains. It turns out that that the …

For the three-dimensional incompressible Navier–Stokes equations, we present a
formulation featuring velocity, vorticity and helical density as independent variables. We find …

We study the long-time behavior of spatially periodic solutions of the Navier–Stokes
equations in the three-dimensional space. The body force is assumed to possess an …

We show that if velocity and vorticity are orthogonal at each point (and they become
orthogonal fast enough) then solutions of the 3D Navier–Stokes equations are smooth. This …

This paper develops further and systematically the asymptotic expansion theory that was
initiated by Foias and Saut in (Ann Inst H Poincaré Anal Non Linéaire, 4 (1): 1–47 1987). We …

The long-time behavior of solutions of the three-dimensional Navier–Stokes equations in a
periodic domain is studied. The time-dependent body force decays, as time t tends to infinity …

We present a rigorous numerical analysis and computational tests for the Galerkin finite
element discretization of the velocity-vorticity-helicity formulation of the equilibrium Navier …

This paper studies, in fine details, the long-time asymptotic behavior of decaying solutions of
a general class of dissipative systems of nonlinear differential equations in complex …

This paper establishes bounds on norms of all orders for solutions on the global attractor of
the 2D Navier–Stokes equations, complexified in time. Specifically, for periodic boundary …

We study the precise asymptotic behavior of a non-trivial solution that converges to zero, as
time tends to infinity, of dissipative systems of nonlinear ordinary differential equations. The …