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Creators/Authors contains: "Sosoe, Philippe"

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  1. ; ; (, Transactions of the American Mathematical Society, Series B)
    We study the stochastic Korteweg-de Vries equation (SKdV) with an additive space-time white noise forcing, posed on the one-dimensional torus. In particular, we construct global-in-time solutions to SKdV with spatial white noise initial data. Due to the lack of an invariant measure, Bourgain’s invariant measure argument is not applicable to this problem. In order to overcome this difficulty, we implement a variant of Bourgain’s argument in the context of an evolution system of measures and construct global-in-time dynamics. Moreover, we show that the white noise measure with variance 1 + t 1+t is an evolution system of measures for SKdV with the white noise initial data. 
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  2. ; ; (, Communications in Mathematical Physics)
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  3. ; ; (, The Annals of Probability)
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  4. ; (, The Annals of Applied Probability)
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  5. ; (, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques)
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  6. ; ; (, Communications on Pure and Applied Mathematics)
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  7. ; ; ; (, Stochastics and Partial Differential Equations: Analysis and Computations)
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