Abstract
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.
The work of E.F. was supported by Grant 201/08/0315 of GA ČR as a part of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.
The work of A.V. was partially supported by the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503., and by the NSF Grant DMS 0607953.
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Feireisl, E., Vasseur, A. (2009). New Perspectives in Fluid Dynamics: Mathematical Analysis of a Model Proposed by Howard Brenner. In: Fursikov, A.V., Galdi, G.P., Pukhnachev, V.V. (eds) New Directions in Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0152-8_9
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DOI: https://doi.org/10.1007/978-3-0346-0152-8_9
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