Global existence for weakly coupled systems of semi-linear structurally damped $\sigma$-evolution models with different power nonlinearities

Abstract

In this paper, we study the Cauchy problems for weakly coupled systems of semi-linear structurally damped $\sigma$-evolution models with different power nonlinearities. By assuming additional $L^m$ regularity on the initial data, with $m\in [1,2)$, we use $(L^m\cap L^2)-L^2$ and $L^2-L^2$ estimates for solutions to the corresponding linear Cauchy problems to prove the global (in time) existence of small data Sobolev solutions to the weakly coupled systems of semi-linear models from suitable function spaces.

arXiv commentarXiv admin note: text overlap with arXiv:1808.02706