高维高阶非线性抛物方程整体解的存在性

The existence of the global solution to the nonlinear parabolic equation with high order in high dimension

在三维空间中考虑带高阶非线性项的复Ginzburg-Landau方程,通过引入权空间,应用内插不等式和先验估计,获得复Ginzburg-Landau方程整体解的存在性,更进一步,使用在权空间算子分解的方法,通过构造紧的正向不变吸收集,建立了整体强吸引子的存在性。

By considering the complex Ginzburg-Landau equation with high order and nonlinear term in three dimensions,by introducing the weighted space and interpolating inequality and prior estimate,the existence of the global solution of the complex Ginzburg-Landau equation is obtained.By further using the method of decomposing operator in wieghted space and constructing compact positively invariant sets,the existence of the strong global attractor is established.