Global weak solutions of nonlinear rotation-Camassa-Holm model

A nonlinear rotation-Camassa-Holm equation, physically depicting the motion of equatorial water waves and having the Coriolis effect, is investigated. Using the viscous approximation tool, we obtain an upper bound estimate about the space derivative of the viscous solution and a high order integrable estimate about the time-space variables. Utilizing these two estimates, we prove that there exist H1(R) global weak solutions to the rotation-Camassa-Holm model.

Automated summary

This paper investigates the nonlinear rotation-Camassa-Holm equation with the Coriolis effect, which physically depicts the motion of equatorial water waves. With the help of the viscous approximation tool, upper bound estimates for the space derivative of the viscous solution and high order integrable estimates for the time-space variables are obtained. Using these two estimates, the existence of H1(R) global weak solutions to the rotation-Camassa-Holm model is proven.