齐次Fourier-Besov-Morrrey空间上广义磁流体力学方程组的存在性和渐近稳定性

Existence and Asymptotic Stability for the Generalized Magneto-Hydrodynamic Equations in Fourier-Besov-Morrrey Spaces

考虑了R^n上n维广义磁流体力学方程组,当初值("_0,d_0)∈FN_(r,λ,∞)^(-β)×FN_(r,λ,∞)^(-β)时,广义磁流体力学方程组对应的Cauchy问题的存在性和渐近稳定性,其中1≤r≤∞,0≤λ≤n或者1≤r≤∞,λ=0以及n≥3,1/2≤σ=α≤(n+2)/4-(n-λ)/(4r),β=2σ-1+(n-λ)/r-n.最后,得到了广义磁流体力学方程组一类自相似解的渐近稳定性.

In this article, we show global existence and asymptotic stability as the time variable escapes to infinity of solutions to the generalized magneto-hydrodynamic equations with small initial data （u0, d0） ∈FN r,λ,∞ -β×FN r,λ,∞ -β n≥3,1/2〈σ=α〈n＋2/4-n-λ/4r,β=2σ-1＋n-λ/r-n. for 1≤r≤∞ ,0〈λ〈n or 1〈r≤∞,λ=0.Also, we obtain a class of asymptotically existence of a basin of attraction for each self-similar solutions with homogeneous initial data.