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Low Mach number limit of the full Navier-Stokes equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Alazard, Thomas |
| Copyright Year | 2006 |
| Abstract | The low Mach number limit for classical solutions of the full Navier-Stokes equations is here studied. The combined effects of large temperature variations and thermal conduction are taken into account. In particular, we consider general initial data. The equations lead to a singular problem whose linearized is not uniformly well-posed. Yet, it is proved that the solutions exist and are uniformly bounded for a time interval which is independent of the Mach number Ma ∈ (0, 1], the Reynolds number Re ∈ [1, +∞] and the Péclet number Pe ∈ [1, +∞]. Based on uniform estimates in Sobolev spaces, and using a Theorem of G. Métivier and S. Schochet [30], we next prove that the penalized terms converge strongly to zero. This allows us to rigorously justify, at least in the whole space case, the well-known computations given in the introduction of the P.-L. Lions’ book [26]. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.ens.fr/~alazard/Arma.pdf |
| Alternate Webpage(s) | https://hal.archives-ouvertes.fr/hal-00153152/document |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0501386v1.pdf |
| Alternate Webpage(s) | http://www-sop.inria.fr/smash/LOMA/Talks/alazard.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Arabic numeral 0 Computation Converge Estimated Lions' Commentary on UNIX 6th Edition, with Source Code Navier–Stokes equations Singular Solutions Well-posed problem Whole Earth 'Lectronic Link |
| Content Type | Text |
| Resource Type | Article |
