White-Noise-Driven KdV-Type Boussinesq System

Aissa Boukarou, Safa M. Mirgani (), Khaled Zennir, Keltoum Bouhali and Sultan S. Alodhaibi
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Aissa Boukarou: University of Science and Technology Houari Boumediene, Algiers 16000, Algeria
Safa M. Mirgani: Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
Khaled Zennir: Department of Mathematics, College of Science, Qassim University, Buraydah 52531, Saudi Arabia
Keltoum Bouhali: Department of Mathematics, College of Science, Qassim University, Buraydah 52531, Saudi Arabia
Sultan S. Alodhaibi: Department of Mathematics, College of Science, Qassim University, Buraydah 52531, Saudi Arabia

Mathematics, 2025, vol. 13, issue 11, 1-14

Abstract: The white-noise-driven KdV-type Boussinesq system is a class of stochastic partial differential equations (SPDEs) that describe nonlinear wave propagation under the influence of random noise—specifically white noise—and generalize features from both the Korteweg–de Vries (KdV) and Boussinesq equations. We consider a Cauchy problem for two stochastic systems based on the KdV-type Boussinesq equations. For these systems, we determine sufficient conditions to ensure that this problem is locally and globally well posed for initial data in Sobolev spaces by the linear and bilinear estimates and their modification together with the Banach fixed point.

Keywords: stochastic; KdV–Boussinesq equation; white noise; Bourgain space; nonlinear equations; energy and industry; well-posedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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