TRAVELING WAVE-LIKE SOLUTIONS OF THE NAVIER-STOKES AND THE RELATED EQUATIONS

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.