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- W2146809306 abstract "This paper furthers the study of Adhikari et al. (2010) [2] on the global regularity issue concerning the 2D Boussinesq equations with vertical dissipation and vertical thermal diffusion. It is shown here that the vertical velocity v of any classical solution in the Lebesgue space L q with 2 ⩽ q < ∞ is bounded by C 1 q for C 1 independent of q . This bound significantly improves the previous exponential bound. In addition, we prove that, if v satisfies ∫ 0 T sup q ⩾ 2 ‖ v ( ⋅ , t ) ‖ L q 2 q d t < ∞ , then the associated solution of the 2D Boussinesq equations preserve its smoothness on [ 0 , T ] . In particular, ‖ v ‖ L q ⩽ C 2 q implies global regularity." @default.
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- W2146809306 date "2011-09-01" @default.
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- W2146809306 title "Global regularity results for the 2D Boussinesq equations with vertical dissipation" @default.
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- W2146809306 doi "https://doi.org/10.1016/j.jde.2011.05.027" @default.
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