论文标题
加权Sobolev空间中的广义分数KDV方程
The generalized fractional KdV equation in weighted Sobolev spaces
论文作者
论文摘要
这项工作涉及多项式加权空间中持久性属性的研究，用于在任何空间尺寸$ d \ geq 1 $中的广义分数KDV方程的解决方案。通过建立良好的态度与某些无限无限持续原理的某些渐近性结合，可以验证分散效应和维度主要确定该模型解决方案允许的最大空间衰变。特别是，我们在加权空间上恢复并扩展了一些已知的结果，例如Benjamin-Ono方程以及分散概括的Benjamin-Ono方程。线性方程获得的估计值似乎具有独立的兴趣，并且对于获得具有不同非线性的模型的加权空间中的持久性能是有用的，该模型是与具有联合非线性的分数KDV方程。
This work concerns the study of persistence property in polynomial weighted spaces for solutions of the generalized fractional KdV equation in any spatial dimension $d\geq 1$. By establishing well-posedness results in conjunction with some asymptotic at infinity unique continuation principles, it is verified that dispersive effects and dimensionality mainly determine the maximum spatial decay allowed by solutions of this model. In particular, we recover and extend some known results on weighted spaces for different models such as the Benjamin-Ono equation, and the dispersion generalized Benjamin-Ono equation. The estimates obtained for the linear equation seem to be of independent interest, and they are useful to obtain persistence properties in weighted spaces for models with different nonlinearities as the fractional KdV equation with combined nonlinearities.
