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

Tuan Anh Dao

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arXiv · 1809.06744

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

Tuan Anh Dao

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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.

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Tuan Anh Dao. 2018-09-17. Global existence for weakly coupled systems of semi-linear structurally damped $\sigma$-evolution models with different power nonlinearities. https://arxiv.org/abs/1809.06744

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