The existence and uniqueness of very weak solutions of the stationary Boussinesq system

We consider the Dirichlet problem for the stationary Boussinesq system in a bounded smooth domain ΩΩ in Rn, where n=2n=2 or 33. We first prove the existence of very weak solutions for arbitrarily large boundary data in W−1/q,q(∂Ω)×W−1/r,r(∂Ω), provided that 3≤q,r<∞3≤q,r<∞ if n=3n=3 and 2