On the vanishing theorems for the discretely self-similar solutions to the Hall equations

摘要

Discretely self-similar solution is a generalized notion of the usual self-similar solution. For the self-similar transformed system of the Hall equations any time periodic solution corresponds to a discretely self-similar solution of the original Hall equations. We prove two types of vanishing theorems for the self-similar Hall equations. One is a Luiville type theorem, which shows triviality of solutions under suitable decay conditions at spatial infinity, and the other one is a unique continuation type of theorem, which shows also triviality of solutions under suitable vanishing condition on at the coordinate origin. The proofs of these results are based on the maximum principle.