We consider two nonlinear (damped and undamped) partial differential equations which model, among other systems from fluid dynamics, special solutions of the n-dimensional incompressible Euler equations. We show that the incorporation of damping effects may or may not suppress the finite-time blowup that occurs in solutions of the associated undamped equation. In particular, we discuss how the amount of damping required to suppress blowup is determined by a relaxation time which depends on the blowup time of solutions of the undamped system.