Lifespan estimates of 1D non-gauge invariant semilinear semirelativistic equations

Abstract

In this paper, the non-global solvability of the Cauchy problem for non-gauge invariant semilinear semirelativistic equations is considered. The lifespan estimate has been considered based on the analogy of semilinear Schrödinger equations and will be determined by the scaling property of semilinear semirelativistic equations. On the other hand, in this paper, in the one-dimensional case, a sharper lifespan estimate is given by a simple argument of weak form with special test functions. Specifically, this lifespan estimate follows from the conjecture of advection equations instead of the scaling property of semilinear semirelativistic equations.