Well-Posedness for a System of Generalized KdV-Type Equations Driven by White Noise

  1. Aissa Boukarou
  2. Mohammadi Begum Jeelani
  3. Nouf Abdulrahman Alqahtani
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Abstract

In this paper, we investigate the Cauchy problem for the coupled generalized Korteweg–de Vries system driven by a cylindrical Wiener process. We prove local well-posedness for data in Hs×Hs, with s>12. The key methods that we used in this paper are multilinear estimates in Bourgain spaces, the Itô formula, and a fixed-point argument.

Article activity feed

  1. Version published to 10.3390/axioms14120911
  2. Version published to 10.20944/preprints202511.0217.v1