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