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arXiv · 1904.00437

Uniqueness result for the 3-D Navier-Stokes-Boussinesq Equations with Horizontal Dissipation

Pierre Dreyfuss·Haroune Houamed
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Abstract

In this paper, for the 3-D Navier-Stokes-Boussinesq system with horizontal dissipation, where there is no smoothing effect on the vertical derivatives, we prove a uniqueness result of solutions $ (u,\rho)\in L^{\infty}_T\big( H^{0,s}\times H^{0,1-s}\big)$ with $ (\nabla_h u,\nabla_h\rho)\in L^{2}_T\big( H^{0,s}\times H^{0,1-s}\big)$ and $s\in [1/2,1]$. As a consequence, we improve the conditions stated in the paper \cite{Miao} in order to obtain a global well-posedness result in the case of axisymmetric initial data.

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Pierre Dreyfuss, Haroune Houamed. 2019-03-31. Uniqueness result for the 3-D Navier-Stokes-Boussinesq Equations with Horizontal Dissipation. https://doi.org/10.1007/s00021-020-00547-x

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