Vigneron, François (2006) Localisation and decay properties of the fields of fluid and plasma mechanics. Function spaces associated to a familly of vector fields. PhD thesis CMAT, CMAT, EP/X p.184.
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Abstract
The first part deals with the spatial asymptotical behavior of solutions of the incompressible Navier-Stokes system. The main results are the propagation of the initial decay in optimal weighted spaces and an asymptotic formula for the velocity and the pressure, which is similar to Bernoulli's formula. The results hold also for MHD.
The second part is devoted to Sobolev spaces constructed from a family of vector fields of subelliptic type. The main results are a description of fractional regularity through the Subriemannian distance, the proof of Hardy-type inequalities and, for the Heisenberg group, a complete theory of traces on a generic caracteristic hypersurface.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| Thesis Supervisor: | Chemin, Jean-Yves |
| Date: | November 2006 |
| Board of examiners: | Claude, Bardos and Jean-Michel, Bony and Guy, David and Hervé, Pajot and Vladimir, Sverak |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | CMAT |
| Collection (Fonds): | EP/X |
| Institution: | EP/X |
| Department: | CMAT |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Localisation, Decroissance, Asymptotique, Navier-stokes, Mhd, Espaces a poids, Espaces de sobolev, Regularites fractionnaires, Condition de crochet (hormander), Somme de carres de champs de vecteurs, Inegalite de hardy, Traces, Groupe de heisenberg |
| ID Code: | 2034 |
|---|---|
| Deposited By: | Laurence Vidament |
| Deposited On: | 11 December 2006 |
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