Weak-renormalized solution for a nonlinear Boussinesq system
Weak-renormalized solution for a nonlinear Boussinesq system
We give a few existence results of a weak-renormalized solution for a class of nonlinear Boussinesq systems: \begin{eqnarray*} & \dfrac{\partial u}{\partial t}+(u\cdot\nabla)u- 2 \textrm{ div } (\mu(\theta) D u)+\nabla p= F(\theta) & \textrm{ in } \Omega\times(0,T),\\ & \dfrac{\partial b(\theta)}{\partial t}+u\cdot\nabla b(\theta)-\Delta \theta = 2 \mu(\theta) |D u |^2 & \textrm{ …