  The aim of this manuscript is to study the influence of the vorticity on the
existence time in fluid systems for which global smoothness and decay is known
in the case of small irrotational data. We focus on two examples: the
Euler-Korteweg system and the two-fluid Euler Maxwell system. We prove that the
lower bound of the lifespan of these systems is no less than the inverse of the
$H^s$ $(s>5/2)$ norm of the rotational part of the initial velocity. Our
approach is based on energy estimates and the fast time decay results of global
solutions to these systems with small irrotational initial data.
