The pressureless Navier-Stokes equations for non-Newtonian fluid are studied.The analytical solutions with arbitrary time blowup,in radial symmetry,are constructed in this paper.With the previous results for the analytical blowup solutions of the N-dimensional（N ≥ 2） Navier-Stokes equations,we extend the similar structure to construct an analytical family of solutions for the pressureless Navier-Stokes equations with a normal viscosity term ▽·（μ（ρ）|▽ u|α▽ u）.
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