Well-posedness and large deviations of the stochastic modified Camassa-Holm equation (Q309006)

The authors consider the stochastic modified Camassa-Holm equation with multiplicative noise \[ dm +[(u^2-u_x^2)m_x+2u_xm^2 +\gamma u_x]dt=udW \] with initial condition \(u(0,x)=u_0(x)\), in which \(W\) is a Wiener process with a nuclear covariance operator \(Q\). In order to establish the well-posedness, the authors introduce a regularized system and prove that the solution of this system constitutes a Cauchy sequence which is convergent to the the solution of the above equation. Finally, they prove a large deviation principle for this stochastic equation.