Well-Posedness of the Stochastic Fractional Boussinesq Equation With Lévy Noise

This article is devoted to the well-posedness of the stochastic fractional Boussinesq equation with Lévy noise. The commutator estimates are applied to overcome the difficulty in the convergence since the nonlocal fractional diffusion has lower regularity. Based on stopping time technique, weak convergence method, and monotonicity arguments, the global existence and uniqueness of the weak solution are obtained in a fixed probability space.