Forced Oberbeck-Boussinesq equations with a Newtonian gravity term have infinitely many weak solutions with the same zero initial data.
Large self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field
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The Navier-Stokes system for an incompressible fluid coupled with the equation for a heat transfer is considered in the whole three dimensional space. This system is invariant under a suitable scaling. Using the Leray-Schauder theorem and compactness arguments, we construct self-similar solutions to this system without any smallness assumptions imposed on homogeneous initial conditions.
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Non-uniqueness of Oberbeck-Boussinesq System with Gravitational Field
Forced Oberbeck-Boussinesq equations with a Newtonian gravity term have infinitely many weak solutions with the same zero initial data.