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Consequences of the choice of a particular basis of $L^2(S^3)$ for the cubic wave equation on the sphere and the Euclidean space

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  • In this paper, the almost sure global well-posedness of the cubic non linear wave equation on the sphere is studied when the initial datum is a random variable with values in low regularity spaces. The result is first proved on the 3D sphere, thanks to the existence of a uniformly bounded in $L^p$ basis of $L^2(S^3)$ and then it is extended to $R^3$ thanks to the Penrose transform.
    Mathematics Subject Classification: 35L05.


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