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Dynamic of rotating fluid layers: \(L^2\)-absorbing sets and onset of convection

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Abstract

Via the longtime behavior of the perturbations to thermal conduction solution \(m_0\), the nonlinear longtime behavior of Navier–Stokes fluid mixtures filling horizontal rotating layers uniformly heated from below and salted by one salt—either from above or below—is investigated. Via the existence of \(L^2\)-absorbing sets, it is shown that the perturbations to \(m_0\) are ultimately bounded. The onset of steady or oscillatory convection is analyzed. Via a Linearization Principle (Rionero in Rend Lincei Mat Appl 25:1–44, 2014) it is shown that the linear theory captures completely the physics of the problem since the linear stability implies the nonlinear global asymptotic stability in the \(L^2\)-norm.

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Authors and Affiliations

  1. Department of Mathematics and Applications “R. Caccioppoli”, University of Naples Federico II, Via Cinzia, 80126, Naples, Italy

    Roberta De Luca

  2. Accademia Nazionale dei Lincei, Via della Lungara 10, 06165, Rome, Italy

    Salvatore Rionero

Authors
  1. Roberta De Luca
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  2. Salvatore Rionero
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Correspondence to Roberta De Luca.

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De Luca, R., Rionero, S. Dynamic of rotating fluid layers: \(L^2\)-absorbing sets and onset of convection. Acta Mech 228, 4025–4037 (2017). https://doi.org/10.1007/s00707-017-1943-z

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  • DOI: https://doi.org/10.1007/s00707-017-1943-z

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