三维导数Ginzburg-Landau方程的整体存在性

The global existence of three-dimension derivative Ginzburg Landau equation

通过技巧性较强的先验估计 ,研究在周期边界条件下的导数 Ginzburg- L andau方程 (CGL ) ut=ρu +(1+iv)Δu - (1+iμ) |u|2σu +αλ1 . (|u|2 u) +β(λ2 . u) |u|2 .其中 u(x)是定义在空间 R3+ 1的未知复值函数 ,Δ是R3的拉普拉斯算子 ,数据ρ >0 ,v,μ是实参数 ,Ω是 R3中的有界区域。获得参数精确的取值范围 。

By the priori estimation of relatively strong technique, derivative Ginzburg Landau equation (CGL) is studied under the periodic boundary condition: u\-t=ρu+(1+iυ)Δu-(1+iμ)|u|\+\{2σ\}u+αλ\-1·(|u|\+2u)+β(λ\-2·u)|u|\+2 Where u(x) is an unknown complex value function defined in space R\+\{3+1\},Δis a Laplacian of R\+3, where ρ>0,υ,μ are real parameters Ω is an area of R\+3 The precise range of parameters' value is obtained and the existence of the initian value problem solution is futher expounded