  We study the well-posedness and the spatial behavior at infinity of perfect
fluid flows on $\R^d$ with initial data in a scale of weighted Sobolev spaces
that allow spatial growth/decay at infinity as $|x|^\beta$ with $\beta<1/2$. In
particular, we show that the solution of the Euler equation generically
develops an asymptotic expansion at infinity with non-vanishing asymptotic
terms that depend analytically on time and the initial data. We identify the
evolution space for initial data in the Schwartz class with a certain space of
symbols.
