Well-posedness for stochastic Camassa-Holm equation

作者：Chen Yong; Gao Hongjun; Guo Boling

来源：Journal of Differential Equations, 2012, 253(8): 2353-2379.

DOI：10.1016/j.jde.2012.06.023

• Stochastic Camassa-Holm equation
• Bourgain spaces
• Regularization
• Fourier restriction norm

The Camassa-Holm equation describes the unidirectional propagation of waves at the free surface of shallow water under the influence of gravity. Due to uncertainty in the modelling and external environment, this modelling could be subject to random fluctuations. In this article, the stochastic Camassa-Holm equation with additive noise is considered. Using regularization, a local existence and uniqueness result in the Sobolev space H-s (R) with s > 3/2 of stochastic Camassa-Holm equation is obtained. With the help of priori estimates, the local solution will blow up in H-q (R) in finite time for any q > 3/2 when initial value satisfies some conditions.

• 出版日期2012-10-15
• 单位北京应用物理与计算数学研究所; 南京师范大学