| Abstract: |
| This talk presents a summary of recent findings on nonrelativistic limit of nonlinear Dirac equations. The discussion is divided into two main parts. Firstly, we discuss the ground states of nonlinear Dirac equations without constraints, focusing on the nonrelativistic limit of these ground states and the convergence behavior in cases with different potentials. Secondly, we delve into the nonrelativistic limit of normalized solutions of nonlinear Dirac equations. Specifically, we demonstrate that the first two components of the normalized ground states converge to the normalized ground states of the corresponding nonlinear Schr\odinger equations and the last two components converges to trivial states. This talk aims to provide an overview of the pertinent findings in this domain. |
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