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Large self-similar solutions to Oberbeck-Boussinesq system with Newtonian gravitational field

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arxiv 2311.01093 v2 pith:4KIHJKZZ submitted 2023-11-02 math.AP

Lorenzo Brandolese (UCBL , ICJ , EDPA) , Grzegorz Karch This is my paper · ORCID
classification math.AP
keywords systemself-similarsolutionsargumentsassumptionscompactnessconditionsconsidered
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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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  1. Non-uniqueness of Oberbeck-Boussinesq System with Gravitational Field

    math.AP 2024-11 conditional novelty 6.0 of 10

    Forced Oberbeck-Boussinesq equations with a Newtonian gravity term have infinitely many weak solutions with the same zero initial data.

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