Abstract
In this paper, we establish two new global Carleman estimates for the linear stochastic Kuramoto–Sivashinsky equations. The first one is for the backward linear stochastic Kuramoto–Sivashinsky equation. Based on this estimate and the duality argument, we obtain the null controllability of the forward linear stochastic Kuramoto–Sivashinsky equation by three controls, one is an internal control in the diffusion term and the others are boundary controls. The second one is for the forward linear stochastic Kuramoto–Sivashinsky equation. According to this estimate, we obtain a unique continuation property for the forward linear stochastic Kuramoto–Sivashinsky equation.
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