In this paper,the existence and uniqueness and the large time asymptotic behavior of the solution for the Eulerbernoulli equation with initialvalue conditions are considered. By using the theory of Sobolev spaces and the contraction mapping principle,we proved that the Eulerbernoulli equation possesses a unique global solution u∈C([0,∞)；Lp(Rn)∩L1,a (Rn))∩C((0,∞)；L∞(Rn)) when the initial data u0,u1∈Lp(R)∩L1.a(R)(in whichσ>1,a∈(0,1],p>σ)and its norm‖u0‖L1.a+‖u0‖Lp+‖u1‖L1.a+‖u1‖Lp is small enough.Moreover the solution u(t,x)has the following large time asymptotic behavior whereO and
