论文标题
第四阶schrödinger方程的时间可整合加权分散估计在三个维度
Time integrable weighted dispersive estimates for the fourth order Schrödinger equation in three dimensions
论文作者
论文摘要
我们考虑第四阶Schrödinger操作员$ h =δ^2+v $，并表明，如果在绝对连续的$ h $中没有特征值或共鸣，则解决方案运算符$ e^{ - ith} $满足大时的$ e^{ - ith} $可以满足大时的$ | t | t | t |^{ - \ frac54} $ decay rate vartess fordeed spaces之间。这种界限改善了两个方向上的自由案例的可能性；更好的时间衰减和较小的空间重量。 In the case of a mild resonance at zero energy, we derive the operator-valued expansion $e^{-itH}P_{ac}(H)=t^{-\frac34} A_0+t^{-\frac54}A_1$ where $A_0:L^1\to L^\infty$ is an operator of rank at most four and $A_1$ maps between多项式加权空间。
We consider the fourth order Schrödinger operator $H=Δ^2+V$ and show that if there are no eigenvalues or resonances in the absolutely continuous spectrum of $H$ that the solution operator $e^{-itH}$ satisfies a large time integrable $|t|^{-\frac54}$ decay rate between weighted spaces. This bound improves what is possible for the free case in two directions; both better time decay and smaller spatial weights. In the case of a mild resonance at zero energy, we derive the operator-valued expansion $e^{-itH}P_{ac}(H)=t^{-\frac34} A_0+t^{-\frac54}A_1$ where $A_0:L^1\to L^\infty$ is an operator of rank at most four and $A_1$ maps between polynomially weighted spaces.
