.　This　paper　investigates　the　globally　dynamic　stabilizing　effects　of　the　geometry　of　the　domain　at　which　the　flow　locates　and　of　the　geometrical　structure　of　the　finite-energy　solutions　to　three-dimensional　(3D)　incompressible　Navier-Stokes　and　Euler　systems.　We　have　established　the　global　existence　and　uniqueness　of　the　smooth　solution　to　the　Cauchy　problem　for　3D　incompressible　Navier-Stokes　and　Euler　equations　for　a　class　of　smooth　large　initial　data　in　orthogonal　curvilinear　coordinate　systems,　which　has　no　smallness　assumption　on　initial　data　for　the　Cartesian　coordinate　system.　Moreover,　we　have　also　established　the　existence,　uniqueness,　and　exponential　decay　rate　of　the　global　strong　solution　to　the　initial-boundary-value　problem　for　3D　NavierStokes　equations　for　a　class　of　smooth　large　initial　data　and　a　class　of　special　bounded　domain　in　orthogonal　curvilinear　coordinate　systems.　Regarding　application,　some　new　classes　of　large-amplitude　global　smooth　solutions　with　very　complex　geometric　structures,　and　that　are　either　non-axisymmetric　or　non-helical　in　R3,　have　been　established　for　3D　incompressible　Navier-Stokes　and　Euler　equations.　This　is　the　first　result　on　the　global　existence　and　uniqueness　of　the　large　smooth　solution　to　3D　incompressible　Navier-Stokes　and　Euler　equations　in　general　orthogonal　curvilinear　coordinate　systems.