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Generalized KdV equation subject to a stochastic perturbation

  • * Corresponding author: Annie Millet

    * Corresponding author: Annie Millet 

Dedication: In the memory of Igor Chueshov

The second author is supported by NSF CAREER grant # 1151618

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  • 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 $L^2(\mathbb{R})$ and the covariance operator is Hilbert-Schmidt in an appropriate Sobolev space, then the solutions with $H^1(\mathbb{R})$ initial data are globally well-posed in $H^1(\mathbb{R})$. This extends results obtained by A. de Bouard and A. Debussche for the stochastic KdV equation.

    Mathematics Subject Classification: Primary: 60H15, 35R60, 35Q53; Secondary: 35L75, 37K10.

    Citation:

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