D. Chae et P. Dubovskii, TRAVELING WAVE-LIKE SOLUTIONS OF THE NAVIER-STOKES AND THE RELATED EQUATIONS, Journal of mathematical analysis and applications, 204(3), 1996, pp. 930-939
We present a new family of travelling wave-like solutions to the Navie
r-Stokes equations of incompressible fluid flows, and other regularize
d equations of the Euler equations, obtain their trend to the solution
s of the Euler equations as the viscosity tends to zero, and estimate
the rate of convergence. We also find a ''singularizing effect'' of th
e viscosity term in the Navier-Stokes equations, i.e., we have a local
moving blow-up of unbounded solutions with the blow-up's speed depend
ing on viscosity. We demonstrate that if the initial function is the B
eltrami flow then the solution of the Navier-Stokes equations conserve
s the Beltrami flow property for all time. (C) 1996 Academic Press, In
c.