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March  2019, 18(2): 603-623. doi: 10.3934/cpaa.2019030

## Well-posedness issues for some critical coupled non-linear Klein-Gordon equations

 University Tunis El Manar, Faculty of Sciences of Tunis, 2092, Tunis, Tunisia

Received  November 2017 Revised  July 2018 Published  October 2018

The initial value problem for some coupled non-linear wave equations is investigated. In the defocusing case, global well-posedness and ill-posedness results are obtained. In the focusing sign, the existence of global and non global solutions are discussed via the potential-well theory. Finally, strong instability of standing waves are established.

Citation: Radhia Ghanmi, Tarek Saanouni. Well-posedness issues for some critical coupled non-linear Klein-Gordon equations. Communications on Pure & Applied Analysis, 2019, 18 (2) : 603-623. doi: 10.3934/cpaa.2019030
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