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In this paper , we first consider the following n (n ≥ 2) -dimensional inviscid incompressible fluid Euler equation : where , υ = (υ1, υ2 ..... υn). Υj = υj (xt), j = 1,2 , ..., n is the velocity of the fluid , pp (xt) is the fluid pressure : υ0 is given initial velocity and meet divυ0 = 0. we get the following result : Theorem 1. (Ⅰ) local existence assuming s gt; n / p 1 and 1 lt; q ≤ p lt; ∞, γ ∈ (1, ∞), n ≥ 2. assuming υ0 ∈ Fp.γs, q and meet diuυ0 = 0. then there exists T = T (║ υ0 ║ Fp.γs, q) gt; 0. such that ( 1 ) has a unique solution υ ∈ C ([0, T]; Fsqpt (Rn)). (Ⅱ) burst criteria assumptions s, p, q, γ satisfy (Ⅰ) conditions , then equation ( 1 ) obtained local solution υ at time T * gt; T blasting : that if, and only after we deal with two-dimensional Boussinesq course system : where vector field υ = (υ1, υ2 ) is the fluid velocity . scalar function θ and π denote the fluid temperature and pressure . α is ( 0,2 ) is a real number , e2 = (0.1). fractional Laplacian | D | α defined for us the main results are as follows : Theorem 2 . Suppose α ∈ (1.2). p ∈ (2. + ∞). Also assume that θo. ∈ Lp ∩ B ∞ .1 o and uo ∈ Lp ∩ B ∞, 1l is zero divergence vector field then the system ( 2 ) has a unique global solution (υ, θ) and satisfies
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