Generalized KDV equation subject to a stochastic perturbation Article

Millet, A, Roudenko, S. (2018). Generalized KDV equation subject to a stochastic perturbation . DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 23(3), 1177-1198. 10.3934/dcdsb.2018147

cited authors

  • Millet, A; Roudenko, S

authors

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 L2(R) and the covariance operator is Hilbert-Schmidt in an appropriate Sobolev space, then the solutions with H1(R) initial data are globally well-posed in H1(R). This extends results obtained by A. de Bouard and A. Debussche for the stochastic KdV equation.

publication date

  • May 1, 2018

published in

Digital Object Identifier (DOI)

start page

  • 1177

end page

  • 1198

volume

  • 23

issue

  • 3