Nonlinear Schrödinger Equation with a Magnetic Potential
The dissipative mechanism of the Schrödinger equation is mathematically described by the decay estimate of solutions. In this talk I mainly focused on the use of harmonic analysis techniques to obtain suitable time decay estimates and then prove the local wellposedness for semilinear Schrödinger equation in certain external magnetic field. It turns out that the scattering with a potential may lead to understanding of the wellposedness of NLS in the presence of nonsmooth or large initial data. Part of this talk is a joint work with Zhenqiu Zhang.
Georgia Institute of Technology PDE Seminar
"Nonlinear Schrödinger Equation with a Magnetic Potential."
Mathematical Sciences Faculty Presentations.