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The motion of one or several rigid bodies in a viscous incompressible fluid has been a topic of numerous theoretical studies. The time evolution of the fluid density ϱf = ϱf (t, x) and the velocityuf = uf...
We study a singular limit for the scaled Navier-Stokes-Fourier system, where the Mach, Froude, and Péclet numbers tend to zero. As a limit problem, we recover a model proposed by Chandrasekhar as a simple alternative to the Oberbeck-Boussinesq system applicable in stellar radiative zones.
We study a model of a compressible, viscous and heat conducting fluid proposed in a series of papers by Howard Brenner. We show that the corresponding system of partial differential equations possesses global-in-time weak solutions for any finite energy initial data. In addition, the density of the fluid remains positive a.a. in the physical domain on any finite time interval.
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