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We study the well-posedness and the spatial behavior at infinity of perfectfluid flows on $\R^d$ with initial data in a scale of weighted Sobolev spacesthat allow spatial growth/decay at infinity as $|x|^\beta$ with $\beta<1/2$. Inparticular, we show that the solution of the Euler equation genericallydevelops an asymptotic expansion at infinity with non-vanishing asymptoticterms that depend analytically on time and the initial data. We identify theevolution space for initial data in the Schwartz class with a certain space ofsymbols.

Perfect fluid flows on $\R^d$ with growth/decay conditions at infinity