Stationary problem of second-grade fluids in three dimensions: existence, uniqueness and regularity
✍ Scribed by J. M. Bernard
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 230 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0170-4214
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✦ Synopsis
This paper is devoted to the stationary problem of second-grade #uids, in the case where # "0, in three dimensions. In relation to the problem in two dimensions, studied by E. H. Ouazar, the H norm of the velocity, in three dimensions, is not bounded for all data. However, by a special method, using together a H bound of the velocity, a &pseudo-continuous dependence' with respect to the data (e!ective for a small H norm of the velocity) and a polynomial inequality (veri"ed by the H norm of the velocity), we show existence of solutions, uniqueness, continuous dependence with respect to the data, with small data. We also prove further regularity results establishing that this is a classical solution when the datum is small enough and smooth enough.