Laplacian operator with Hardy potential and applications to PDEs
Abstract：In this talk, we first talk about the Sobolev space theory and harmonic analysis tools for the Laplacian opeartor associated with Hardy potential. And then we consider the energy-critical nonlinear wave equation in the presence of an Hardy potential. In the defocusing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold. This part is jointed with Changxing Miao and Jason Murphy. Finally, we study the low regularity problem for 3d cubic wave equation with the Hardy potential. This part is jointed with Changxing Miao and Junyong Zhang.