  We prove the existence of strong solutions to Navier-Stokes equations in
three dimensional thin domains. Our proof is based on the energy and the
Poincar\'e inequalities as well as contraction principle argument and is free
of the mean value operator. The price we pay for the simplicity of the proof
are stronger assumptions on the initial velocity and the forcing term. We need
to assume that their derivatives with respect to time belong to certain
Lebesgue space.
