Convection of a very viscous and non-heat-conductive fluid

The asymptotic model of Oberbeck–Boussinesq convection is considered in the case when the heat conductivity $\delta$ is equal to zero and the viscosity $\mu=+\infty$. The global existence and uniqueness results are proved for the basic initial-boundary-value problem; both classical and generalized solutions are considered. It is shown that each solution approaches an equilibrium as $t\to\mp\infty$.
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