标题： 具有强奇性的三维能量临界非齐次非线性薛定谔方程 显示英文标题

标题： The 3D energy-critical inhomogeneous nonlinear Schrodinger equation with strong singularity

摘要： 本文研究了三维能量临界非齐次非线性薛定谔方程（INLS）的初值问题$$i\partial_{t}u+\Delta u=\pm|x|^{-\alpha}|u|^{4-2\alpha}u$$，其具有强奇异性$3/2\leq \alpha<2$。对于$0<\alpha<3/2$，该适定性问题已有充分理解，但情况$3/2\leq \alpha<2$至今仍未解决。我们通过改进加权空间上的非齐次 Strichartz 估计，解决了$3/2\leq \alpha<11/6$的局部/小数据整体适定性结果。 显示英文摘要

摘要： In this paper, we study the Cauchy problem for the 3D energy-critical inhomogeneous nonlinear Schr\"odinger equation(INLS) $$i\partial_{t}u+\Delta u=\pm|x|^{-\alpha}|u|^{4-2\alpha}u$$ with strong singularity $3/2\leq \alpha<2$. The well-posedness problem is well-understood for $0<\alpha<3/2$, but the case $3/2\leq \alpha<2$ has remained open so far. We address the local/small data global well-posedness result for $3/2\leq \alpha<11/6$ by improving the inhomogeneous Strichartz estimates on the weighted space.