一维二阶非线性薛定谔方程的局部适定性

Local well-posedness of 1-D nonlinear second ordered schr?dinger equation

讨论了一维二阶非线性薛定谔方程在模空间M_(2,p)中的局部适定性问题,通过对频率进行一致分解,将解在全空间中的整体估计转化为单位区间中的局部估计;通过讨论不同频率间的相互关系,运用Strichartz估计和Bilinear Strichart估计得到方程的局部适定性。

Local well-posedness problem is discussed.Through the frequency uniform decomposion of a solution inthe whole space,the global well-posedness estimate of the solution is converted into the unit local well-posednessestimate.By discussing the relationship between different frequency and using the Strichartz estimates and theBilinear Strichartz estimates,the local well-posedness of equation is obtained.