The local existence of strong solution for the stochastic 3D Boussinesq equations

Abstract

Abstract The stochastic 3D Boussinesq equations with additive noise are considered. We prove the local existence of the strong solution in Hs $H^{s}$ ( 12<s≤1 $\frac{1}{2}< s\leq 1$). We also obtain a new stopping time, which shows that the H12+ $H^{\frac{1}{2}^{+}}$ norm of u controls the breakdown of the strong solution. Furthermore, we give the probability estimate of the lifespan larger than δ ( 0<δ<1 $0<\delta <1$).

Keywords

• Stochastic Boussinesq equation
• Strong solution
• Stopping time estimate