Null Controllability of Stochastic Degenerate Parabolic Equation With Convection Term

ABSTRACT This paper concerns the null controllability of stochastic degenerate parabolic equation with convection term in weakly degenerate case. Due to the degeneracy, we first transfer to study an approximate nondegenerate system. Next, we establish the Carleman estimate for backward stochastic degenerate parabolic equation with convection term. In order to deal with the convection term, the Carleman estimate is established by introducing an auxiliary function to transfer the diffusion and the convection term into a whole complex divergence‐like form. By this Carleman estimate, we then obtain an observability inequality for the adjoint system of the approximate system. Based on the observability inequality and an approximate argument, we proved our null controllability result.