Stochastic and Multiscale Modeling and Computation Seminar by Chiun-Chang Lee (National Hsinchu: An Introduction to Schrödinger Equations and Semiclassical Limits (II)
Speaker: Chiun-Chang Lee, National Hsinchu University of Education, Taiwan
Title: An Introduction to Schrödinger Equations and Semiclassical Limits (II)
Abstract: In continuation of the last discussion, I will present a case study on the semiclassical analysis of nonlinear Schrödinger equations. The focus will be on introducing a modulated energy functional to govern mass density and linear momentum, particularly in relation to the compressible Euler equations. Additionally, I will introduce a nonlocal Schrödinger equation, drawing connections to a nonlocal Euler equation through Madelung's transformation. It is important to note that rigorous analysis regarding the convergence and existence of solutions for this nonlocal Euler equation remains an open challenge in my current research. I welcome discussions on this unresolved problem.
Stochastic and Multiscale Modeling and Computation Seminar