Remark on the global non-existence of semirelativistic equations with non-gauge invariant power type nonlinearity with mass

Abstract

The non-existence of global solutions for semirelativistic equations with non-gauge invariant power type nonlinearity with mass is studied in the frame work of weighted $L^1$. In particular, a priori control of weighted integral of solutions is obtained by introducing a pointwise estimate of fractional derivative of some weight functions. Especially, small data blowup with small mass is obtained.

10pages, no figures. arXiv admin note: substantial text overlap with arXiv:1801.04793