ABSTRACT

We consider a model for convection in compressible fluids in two dimensions. A constitutive limit is studied in which both the mechanical compressibility and thermal expansion affect the buoyancy force. The motion is no longer isochoric as in the classical Boussinesq approximation but has a uniform expansion rate associated to the upward motion: $\mathbf{\nabla }\mathbf{\cdot }\mathit{v}=\beta v_z$. By using a perturbative approach, we study a Boussinesq-like approximation with pressure-dependent buoyancy force. The existence of weak solutions for the approximated system is proved and their stability is investigated.

中文翻译：

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具有压力诱导分层密度的流体的近似 à la Oberbeck-Boussinesq

摘要

我们考虑二维可压缩流体中的对流模型。研究了机械压缩性和热膨胀都会影响浮力的本构极限。运动不再像经典的 Boussinesq 近似那样是等容的，而是具有与向上运动相关的均匀膨胀率：$\mathbf{\nabla }\mathbf{\cdot }\mathit{v}=\beta v_z$. 通过使用微扰方法，我们研究了具有与压力相关的浮力的类似 Boussinesq 的近似值。证明了近似系统弱解的存在性，并研究了它们的稳定性。