The Cauchy problem for space-time monopole equations in Sobolev spaces

초록

We consider the initial value problem of space-time monopole equations in one space dimension with initial data in Sobolev space H-s. Observing null structures of the system, we prove local well-posedness in almost critical space. Unconditional uniqueness and global existence are proved for s >= 0. Moreover, we show that the H-1 Sobolev norm grows at a rate of at most c exp(ct(2)). Published by AIP Publishing.

키워드