A Coupled Generalized Korteweg-de Vries System Driven by White Noise

2025/10/27 by Boukarou, Aissa
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.23843

Abstract

In this paper, we investigate the Cauchy problem for the coupled generalized Korteweg-de Vries system driven by white noise. We prove local well-posedness for data in H^s × H^s, with s>1/2. The key ingredients that we used in this paper are multilinear estimates in Bourgain spaces, the Itô formula and a fixed point argument. Our result improves the local well-posedness result of Gomes and Pastor \citegomes2021solitary.

Citations

• Spatial analyticity of solutions for a coupled system of generalized KdV equations
• Solitary wave solutions and global well-posedness for a coupled system\n of gKdV equations
• Introduction to Regularity Structures
• Diophantine Conditions in Well-Posedness Theory of Coupled KdV-Type Systems: Local Theory

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