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      Global well-posedness for the coupled system of Schrodinger and Kawahara equations

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          Abstract

          We study the local and global well-posedness for the coupled system of Schrodinger and Kawahara equations on the real line. The Sobolev space \(L^{2} \times H^{-2}\) is the space where the lowest regularity local solutions are obtained. The energy space is \(H^1 \times H^2\). We apply the Colliander-Holmer-Tzirakis method [7] to prove the global well-posedness in \(L^2 \times L^2\) where the energy is not finite. Our method generalizes the method of Colliander-Holmer-Tzirakis in the sense that the operator that decouples the system is nonlinear.

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          Journal
          02 May 2023
          Article
          2305.01504
          781da5bc-a69a-4b37-9858-4118e29f6259

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          21 pages
          math.AP

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