Well-posedness and the small time large deviations of the stochastic integrable equation governing short-waves in a long-wave model. (June 2016)

• Record Type: Journal Article
• Authors: Chen, Yong; Gao, Hongjun; Fan, Lili
• Is Part Of: Nonlinear analysis. Volume 29(2016)
• Page Start: 38
• Page End: 57
• Publication Date: 2016-06
• Subjects: Stochastic integrable equation -- Well-posedness -- Large deviations -- Regulation -- Trilinear estimate; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.10.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the stochastic integrable equation governing short-waves in a long-wave model. Firstly, the local well-posedness for this system is established by fixed point argument and (bilinear) trilinear estimates. Then the small time asymptotics of the equation is proved. The corresponding results for the stochastic Hunter–Saxton equation can be obtained by the same methods.