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White Noise Driven Korteweg–de Vries Equation

✍ Scribed by A. de Bouard; A. Debussche; Y. Tsutsumi

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
212 KB
Volume
169
Category
Article
ISSN
0022-1236

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✦ Synopsis

We consider a stochastic Korteweg de Vries equation on the real line. The noise is additive. We use function spaces similar to those introduced by Bourgain to prove well posedness results for the Korteweg de Vries equation in L 2 (R). We are able to handle a noise which is locally white in space and time. More precisely, it is a space-time white noise multiplied by an L 2 -function of the space variable. Due to the lack of a priori estimates, we can only get a local existence result in time. However, we obtain the global existence of L 2 (R) solutions when the covariance operator of the noise is Hilbert Schmidt in L 2 (R).

📜 SIMILAR VOLUMES

On the Stochastic Korteweg–de Vries Equa
On the Stochastic Korteweg–de Vries Equation
✍ A de Bouard; A Debussche 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 429 KB

We consider a stochastic Korteweg de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions in H 1 (R) in the case of additive noise and existence of martingales solution