On the stochastic two-component b-family system

ABSTRACT

Considered herein is the stochastic two-component b-family system. The local well-posedness in the Sobolev space with s > 3/2 is established by regularization. Then a Wentzell–Freidlin type large deviation principle (LDP) is established for the regularized system by the weak convergence method. Finally, the exponentially equivalent of the laws is proved, from which the LDP of the stochastic two-component b-family system is obtained.

Keywords:

• Stochastic two-component b-family system
• regularization
• large deviations
• exponentially equivalent

Mathematics Subject Classification:

• 60H15
• 35A08
• 35R60.

Funding

This work is partially supported by China NSF Grant Nos. 11531006, 11401532, and 11501511; PAPD of Jiangsu Higher Education Institutions; Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application; and Zhejiang Provincial NSF of China under Grant Nos. LQ14A010015 and LQ15A010012.