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The classical form of the Navier-Stokes equations system, which is derived from the principle of conservation of mass and momentum, describes the motion of a homogeneous fluid subject to a field of external forces. In this work, we develop a study to find the maximal interval of existence of solutions in time to the Navier-Stokes equations in a three dimensional thin domain, i.e., Ω∞ = ω × (0, ∞), where ω ⊂ R2 e ∞ ∈ (0, 1), considering different combinations of boundary conditions. [ABSTRACT FROM AUTHOR]