  In this paper we use maximum principle in the far field region for the time
dependent self-similar Euler equations to exclude discretely self-similar
blow-up for the Euler equations of the incompressible fluid flows. Our decay
conditions near spatial infinity of the blow-up profile are given explicitly in
terms the coefficient in the equations. We also deduce triviality of the
discretely self-similar solution to the magnetohydrodynamic system(MHD), under
suitable decay conditions near spatial infinity than the previous one. Applying
similar argument directly to the Euler equations, we obtain a priori estimate
of the vorticity in the far field region.
