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Regularity to Boussinesq equations with partial viscosity and large data in three-dimensional periodic thin domain. (English) Zbl 1373.35247

Summary: This paper is devoted to study the partial viscosity Boussinesq equations on a 3D thin periodic domain. The global well-posedness of strong solution with the initial data \((u_0,\theta_0)\in H_{per}^2(\Omega_\epsilon)\times H_{\mathrm{per}}^1(\Omega_\epsilon)\) is established, where \(\Omega_\epsilon=[0,L_1]\times [0,L_2]\times [0,\epsilon]\) is with periodic boundary conditions.

MSC:

35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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