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

초록

We consider the Dirichlet problem for the stationary Boussinesq system in a bounded smooth domain Omega in R-n, where n = 2 or 3. We first prove the existence of very weak solutions for arbitrarily large boundary data in W--1/q,W-q(partial derivative Omega) x W--1/r,W-r(partial derivative Omega), provided that 3 <= q, r < infinity if n = 3 and 2 < q, r < infinity if n = 2. The uniqueness of very weak solutions is also shown for sufficiently small data. (C) 2011 Elsevier Ltd. All rights reserved.

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