  In this paper, we consider the energy conservation of the Leray-Hopf weak
solution $u$ to the Navier-Stokes equations on bounded domains $\Omega$ with
Lipschitz boundary $\partial\Omega$. We prove that although the boundary effect
appears, the Shinbrot's condition $u\in L^q_{loc}((0,T];L^p(\Omega))$ with
$\frac{1}{p}+\frac{1}{q}=\frac{1}{2},p\geq 4$ still guarantees the validity of
energy conservation of $u$, no boundary layer assumptions are required when
dealing with domains with Lipschitz boundary. Compared to the existed methods,
our critical strategies are that we first separate the mollification of weak
solution from the boundary effect by considering non-standard local energy
equality and transform the boundary effects into the estimates of the gradient
of the cut-off functions, then by establishing a sharp $L^2L^2$ estimate for
pressure $P$ and using the zero boundary condition, we obtain global energy
equality by taking suitable cut-off functions. Our result provides a unified
method to deal with domains with or without boundary and improves the
corresponding results in \cite{C-L,Yu}.
