本文考虑如下形式的n维可压缩流体的Navier-Stokes方程(n≥2): (?)_tρ+sum from j=1 to n((?)_j(ρu_j))=0, (?)_tu_i-sum from j=1 to n(ρ~(-1)[μ(?)_j((?)_ju_j+(?)_iu_j)+μ′(?)_i(?)_ju_j])=-sum from j=1 to n(u_j(?)_ju_i-ρ~(-1)(?)_iP(ρ),(1) ρ|_(t=0)=(?)+(?)_0(x),u|_(t=0)=u_0(x),其中t≥0,x=(x_1,…,x_n),ρ为密度,u=(u_1,…,u_n)为速度,μ,μ′为粘性系数,P(ρ)为压力,为一常数,用|·|_s表示Sobolev空间范数。有如下结论: In this paper, we consider the Navier-Stokes equation (n≥2) of an n-dimensional compressible fluid in the following form: (?) _ Tp + sum from j = 1 to n ((?) _j (ρu_j)) = 0, sum from j = 1 to n (ρ -1) [μ (?) _ j (?? _ ju_j + (?) _ iu_j) + μ ’(?) _i (?) _ ju_j]) = - sum from j = 1 to n (u_j (?) _ ju_i-p -1 (?) _ iP (p), (1) p | _ (t = 0) (t = 0) = u_0 (x), where t≥0, x = (x_1, ..., x_n), ρ is the density, u = (u_1, ..., u_n) is the velocity, μ and μ ’are the viscous coefficients, P (ρ) is the pressure, which is a constant, Sobolev space norm is represented by | · | _s. It is concluded as follows: