| Abstract: |
| We study the Boussinesq-B\`enard equations in dimension 3 subject to a multiplicative random perturbation; we have to
add a Brinkman-Fochheimer smoothing term in the evolution equation for the velocity $u$.
We prove that for $H^1$-initial velocity $u_0$ and temperature $\theta_0$ with proper moments, the system of SPDEs is a.s. globally well posed in
$\big( C([0,T];H) \cap L^4(0,T;V)\big) \times \big(C([0,T]; L^2)\cap L^2(0,T;H^1)\big)$. We also prove the existence of higher moments of the solution $(u,\theta)$. |
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