This　paper　investigates　the　globally　dynamical　stabilizing　effects　of　the　geometry　of　the　domain　at　which　the　flow　locates　and　of　the　geometry　structure　of　the　solutions　with　the　finite　energy　to　the　three-dimensional　(3D)　incompressible　Navier-Stokes　(NS)　and　Euler　systems.　The　global　well-posedness　for　large　amplitude　smooth　solutions　to　the　Cauchy　problem　for　3D　incompressible　NS　and　Euler　equations　based　on　a　class　of　variant　spherical　coordinates　is　obtained,　where　smooth　initial　data　is　not　axi-symmetric　with　respect　to　any　coordinate　axis　in　Cartesian　coordinate　system.　Furthermore,　we　establish　the　existence,　uniqueness　and　exponentially　decay　rate　in　time　of　the　global　strong　solution　to　the　initial　boundary　value　problem　for　3D　incompressible　NS　equations　for　a　class　of　the　smooth　large　initial　data　and　a　class　of　the　special　bounded　domain　described　by　variant　spherical　coordinates.