Research article

Osgood type blow-up criterion for the 3D Boussinesq equations with partial viscosity

  • Received: 27 October 2017 Accepted: 12 November 2017 Published: 27 December 2017
  • MSC : 35B44, 35B65, 76D03

  • This paper is dedicated to studying the blow-up criterion of smooth solutions to the three-dimensional Boussinesq equations with partial viscosity. By means of the Littlewood-Paley decomposition, we give an improved logarithmic Sobolev inequality and through this, we obtain the corresponding blow-up criterion in a space larger than $\dot{B}^0_{\infty, \infty}$, which extends several previous works.

    Citation: Zhaoyang Shang. Osgood type blow-up criterion for the 3D Boussinesq equations with partial viscosity[J]. AIMS Mathematics, 2018, 3(1): 1-11. doi: 10.3934/Math.2018.1.1

    Related Papers:

  • This paper is dedicated to studying the blow-up criterion of smooth solutions to the three-dimensional Boussinesq equations with partial viscosity. By means of the Littlewood-Paley decomposition, we give an improved logarithmic Sobolev inequality and through this, we obtain the corresponding blow-up criterion in a space larger than $\dot{B}^0_{\infty, \infty}$, which extends several previous works.


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