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Initial Boundary Value Problem for Two-Dimensional Viscous Boussinesq Equations

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Abstract

We study the initial boundary value problem of two-dimensional viscous Boussinesq equations over a bounded domain with smooth boundary. We show that the equations have a unique classical solution for H 3 initial data and the no-slip boundary condition. In addition, we show that the kinetic energy is uniformly bounded in time.

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Author notes

  1. Kun Zhao

    Present address: Mathematical Biosciences Institute, The Ohio State University, Columbus, OH, 43210, USA

Authors and Affiliations

  1. Department of Mathematics, The University of Georgia, Athens, GA, 30602, USA

    Ming-Jun Lai

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Ronghua Pan

Authors
  1. Ming-Jun Lai
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  2. Ronghua Pan
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  3. Kun Zhao
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Correspondence to Ming-Jun Lai.

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Communicated by C.M. Dafermos

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Lai, MJ., Pan, R. & Zhao, K. Initial Boundary Value Problem for Two-Dimensional Viscous Boussinesq Equations. Arch Rational Mech Anal 199, 739–760 (2011). https://doi.org/10.1007/s00205-010-0357-z

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  • DOI: https://doi.org/10.1007/s00205-010-0357-z

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