Non-uniqueness of Oberbeck-Boussinesq System with Gravitational Field
Xiaoran Liu
TL;DR
This paper demonstrates that the Oberbeck-Boussinesq system with gravity on an unbounded domain can have multiple solutions, using an unstable Navier-Stokes profile to establish non-uniqueness.
Contribution
It introduces a novel approach to show non-uniqueness in the Oberbeck-Boussinesq system by leveraging unstable profiles from Navier-Stokes equations.
Findings
Non-uniqueness of solutions proven for the system
Application of unstable Navier-Stokes profiles
Results on gravitational Oberbeck-Boussinesq system
Abstract
We consider the Oberbeck-Boussinesq system with gravitational force on the whole space. We prove the non-uniqueness of the system applying the unstable profile of Navier-Stokes equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · advanced mathematical theories · Advanced Mathematical Physics Problems