The　time-dependent　Navier-Stokes　equations　with　leak　boundary　conditions　are　investigated　in　this　paper.　The　equivalent　variational　inequality　is　derived,　and　the　weak　and　strong　solvabilities　of　this　variational　inequality　are　obtained　by　the　Galerkin　approximation　method　and　the　regularized　method.　In　addition,　the　continuous　dependence　property　of　solutions　on　given　initial　data　is　established,　from　which　the　strong　solution　is　unique.