Periodic Solutions of the Korteweg-de Vries Equation Driven by White Noise
نویسندگان
چکیده
Abstract. We consider a Korteweg-de Vries equation perturbed by a noise term on a bounded interval with periodic boundary conditions. The noise is additive, white in time and “almost white in space”. We get a local existence and uniqueness result for the solutions of this equation. In order to obtain the result, we use the precise regularity of the Brownian motion in Besov spaces, and the method which was introduced by J. Bourgain, but based here on Besov spaces.
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ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 36 شماره
صفحات -
تاریخ انتشار 2005