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Uniqueness result for the 3-D Navier-Stokes-Boussinesq equations with horizontal dissipation

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, ρ) ∈ L ∞ T H 0,s × H 0,1−s with (h u, h ρ) ∈ L 2 T H 0,s × H 0,1−s and s ∈ [1/2, 1]. As a consequence, we improve the conditions stated in the paper [13] in order to obtain a global well-posedness result in the case of axisymmetric initial data.
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https://hal.archives-ouvertes.fr/hal-02088514
Contributor : Haroune Houamed <>
Submitted on : Tuesday, April 2, 2019 - 11:51:18 PM
Last modification on : Monday, October 12, 2020 - 2:28:06 PM
Long-term archiving on: : Wednesday, July 3, 2019 - 5:54:18 PM

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  • HAL Id : hal-02088514, version 1

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Haroune Houamed, Pierre Dreyfuss. Uniqueness result for the 3-D Navier-Stokes-Boussinesq equations with horizontal dissipation. 2019. ⟨hal-02088514⟩

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