Geodesic
Probabilistic well-posedness for the cubic wave equation
Journal of the European Mathematical Society, Tome 16 (2014) no. 1, pp. 1-30 Cet article a éte moissonné depuis la source EMS Press

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The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs measures), and second, we show that the flow that we are able to construct enjoys very nice dynamical properties, including a new notion of probabilistic continuity.
DOI : 10.4171/jems/426
Classification : 35-XX, 00-XX
Keywords: random series, wave equations, well-posedness 
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     year = {2014},
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Nicolas Burq; Nikolay Tzvetkov. Probabilistic well-posedness for the cubic wave equation. Journal of the European Mathematical Society, Tome 16 (2014) no. 1, pp. 1-30. doi: 10.4171/jems/426

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