AIMS Mathematics, 2018, 3(1): 1-11. doi: 10.3934/Math.2018.1.1

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

School of Mathematical Science, Shanghai Jiao Tong University, Shanghai 200240, P. R. China

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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