Lax Pairs and Isospectral Theory of Euler Equation with Perturbations

Though the global well-posedness of two-dimensional Euler equations with perturbations has been proved,the global well-posedness of three-dimensional Euler equations with perturbations has not been proved,which remains a difficult mathematical problem.The given theorem is supposed to be of some help to the proof of the global well-posedness of three-dimensional Euler equations with perturbations.This paper mainly researches into the Lax pairs of Euler equations with a(t) perturbations,and it also further researches into isospectral theory of Euler equations with such kind of perturbations.