A Note on C^2 Ill-posedness Results for the Zakharov System in Arbitrary Dimension





Zakharov System, $C^2$ ill-posedness


This work is concerned with the Cauchy problem for a Zakharov system with initial data in Sobolev spaces H^k(\R^dH^l(\R^dH^l−1(\R^d).We recall the well-posedness and ill-posedness results known to date and establish new ill-posedness results.We prove C^2 ill-posedness for some new indices (kl) ∈ \R^2. Moreover, our results are valid in arbitrary dimension. We believe that our detailed proofs are built on a methodical approach and can be adapted to obtain similar results for other systems and equations.

Author Biographies

L. Domingues, Universidade Federal do Espírito Santo

Departamento de Matemática Aplicada, CEUNES/UFES

R. Santos, Universidade Federal do Rio de Janeiro

IPoli, Centro Multidisciplinar UFRJ-Macaé


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How to Cite

Domingues, L., & Santos, R. (2023). A Note on C^2 Ill-posedness Results for the Zakharov System in Arbitrary Dimension. Trends in Computational and Applied Mathematics, 24(3), 505–519. https://doi.org/10.5540/tcam.2023.024.03.00505



Original Article