Distribution-valued initial data for the complex ginzburg-landau equation
Distribution-valued initial data for the complex ginzburg-landau equation
复制标题
复杂 ginzburg-landau 方程的分布值初始数据
DOI：
10.1080/03605309708821254
复制
发表时间：
1997
影响因子：
1.9
通讯作者：
M. Oliver
中科院分区：
文献类型：
--
作者：
C. Levermore;M. Oliver
对于Sobolev空间H{sup q}中的分布初始数据，具有d维2{sigma} + 1阶非线性的广义复Ginzburg-Landau （CGL）方程具有唯一的局部经典解，条件是q > d/2 - 1/{sigma}。这一结果与Cazenave和Weissler在1990年证明的非线性薛定谔方程的一个定理直接对应。虽然NLS情况下的证明依赖于Besov空间技术，但这里表明，对于CGL方程，可以通过初等手段简化线性半群的平滑性质以获得几乎最优的结果。1图。
The generalized complex Ginzburg-Landau (CGL) equation with a nonlinearity of order 2{sigma} + 1 in d spatial dimensions has a unique local classical solution for distributional initial data in the Sobolev space H{sup q} provided that q > d/2 - 1/{sigma}. This result directly corresponds to a theorem for the nonlinear Schroedinger (NLS) equation which has been proved by Cazenave and Weissler in 1990. While the proof in the NLS case relies on Besov space techniques, it is shown here that for the CGL equation, the smoothing properties of the linear semigroup can be eased to obtain an almost optimal result by elementary means. 1 fig.