Well-posedness and Large Deviations of the Stochastic Modified Camassa-Holm Equation

作者：Chen, Yong^*; Gao, Hongjun

来源：Potential Analysis, 2016, 45(2): 331-354.

DOI：10.1007/s11118-016-9548-z

• Stochastic modified Camassa-Holm equation
• Well-posedness
• Large deviations
• Regulation
• Trilinear estimate

In this paper, the stochastic modified Camassa-Holm (MCH) equation is concerned. Firstly, the local well-posedness for this equation is established by the trilinear estimates to the approximate solutions. Then the large deviation principle (LDP) for the regularized stochastic MCH is obtained by the weak convergence approach. To get the LDP for stochastic MCH, some exponentially equivalents of the probability measures are proved. The regularization method plays an crucial role.

• 出版日期2016-8
• 单位南京师范大学; 吉林大学; 浙江理工大学