Exponential dichotomy of a strongly continuous cocycle $bFi$ is proved to be equivalent to existence of a Ma~{n}e sequence either for $bFi$ or for its adjoint. As a consequence we extend some of the classical results to general Banach bundles. The dy
namical spectrum of a product of two cocycles, one of which is scalar, is investigated and applied to describe the essential spectrum of the Euler equation in an arbitrary spacial dimension.
We prove that the energy equality holds for weak solutions of the 3D Navier-Stokes equations in the functional class $L^3([0,T);V^{5/6})$, where $V^{5/6}$ is the domain of the fractional power of the Stokes operator $A^{5/12}$.
