能量临界分数阶非线性Schrodinger方程的整体弱解

Global Weak Solutions for Energy-Critical FractionalNonlinear Schr dinger Equations

利用紧性方法给出能量临界分数阶非线性Schr9dinger方程Cauchy问题解的存在性,并证明Cauchy问题存在整体解.通过构造逼近方程,对满足逼近方程的解序列取极限,得到的极限函数即为能量临界分数阶非线性Schr9dinger方程的整体弱解,并证明该弱解满足能量不等式和质量守恒性质.

By using the compactness method,we gaved the existence of solutions to the Cauchy problem of the energy-critical fractio nal nonlinear Schr dinger equation and proved the existence of global solution to the Cauchy problem.By constructing the approximation equation and takin g the limit of the solution sequence satisfying the approximation equation,the obtained limit function was the global weak solution of the energy-critical fractional nonlinear Schr dinger equation,and it was proved that the weak solution satisfied the energy inequality and mass conservation property.