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GENERALIZED KDV EQUATION SUBJECT TO A STOCHASTIC PERTURBATION

Abstract : We prove global well-posedness of the subcritical generalized Korteweg-de Vries equation (the mKdV and the gKdV with quartic power of nonlinearity) subject to an additive random perturbation. More precisely, we prove that if the driving noise is a cylindrical Wiener process on L 2 (R) and the covariance operator is Hilbert-Schmidt in an appropriate Sobolev space, then the solutions with H 1 (R) data are globally wellposed in H 1 (R). This extends results obtained by A. de Bouard and A. Debussche for the stochastic KdV equation. Dedication: In the memory of Igor Chueshov.
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Annie Millet, Svetlana Roudenko. GENERALIZED KDV EQUATION SUBJECT TO A STOCHASTIC PERTURBATION. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2018, 23 (3), pp.1177-1198. ⟨10.3934/dcdsb.2018147⟩. ⟨hal-01519175v2⟩

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