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

L. Domingues, R. Santos

Abstract


This work is concerned with the Cauchy problem for a Zakharov system with initial data in Sobolev spaces H^k(\R^d)×H^l(\R^d)×H^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 (k, l) ∈ \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.


Keywords


Zakharov System; $C^2$ ill-posedness

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References


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DOI: https://doi.org/10.5540/tcam.2023.024.03.00505

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