  In this paper, a new formulation for the three dimensional Euler equations is
derived. Since the Euler system is hyperbolic-elliptic coupled in a subsonic
region, so an effective decoupling of the hyperbolic and elliptic modes is
essential for any development of the theory. The key idea in our formulation is
to use the Bernoulli's law to reduce the dimension of the velocity field by
defining new variables $(1,\beta_2=\frac{u_2}{u_1},\beta_3=\frac{u_3}{u_1})$
and replacing $u_1$ by the Bernoulli's function $B$ through
$u_1^2=\frac{2(B-h(\rho))}{1+\beta_2^2+\beta_3^2}$. We find a conserved
quantity for flows with a constant Bernoulli's function, which behaves like the
scaled vorticity in the 2-D case. More surprisingly, a system of new
conservation laws can be derived, which is new even in the two dimensional
case. We use this new formulation to construct a smooth subsonic Euler flow in
a rectangular cylinder, which is also required to be adjacent to some special
subsonic states.
