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

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  • 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.

    Mathematics Subject Classification: Primary: 35L05; Secondary: 53B44.


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