We　consider　the　global　existence　of　the　two-dimensional　Navier-Stokes　flow　in　the　exterior　of　a　moving　or　rotating　obstacle.　Bogovskii　operator　on　a　subset　of　R-2　is　used　in　this　paper.　One　important　thing　is　to　show　that　the　solution　of　the　equations　does　not　blow　up　in　finite　time　in　the　sense　of　some　L-2　norm.　We　also　obtain　the　global　existence　for　the　2D　Navier-Stokes　equations　with　linearly　growing　initial　velocity.