  We give a new sufficient criteria to prove the uniqueness of the
incompressible Euler equation in dimension $N\geq2$. In their celebrated works
by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\'ekelyhidi Jr.
[7] they have obtained the nonuniqeness of weak solutions of incompressible
Euler equation. Here we obtain uniqueness criteria for the same equation under
some mild regularity condition on weak solutions. Our proof is simple and can
be employed to other equations like inhomogeneous incompressible Euler and
Euler-Boussinesq equations. One of the key ingredients in our proof is
commutator estimate [5, 11].
