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Well-posedness in Gevrey function spaces for the Prandtl equations with non-degenerate critical points
| Content Provider | Semantic Scholar |
|---|---|
| Author | Li, Wei-Xi Yang, Tong |
| Copyright Year | 2019 |
| Abstract | Abstract. In the paper, we study the well-posedness of the Prandtl system without monotonicity and analyticity assumption. Precisely, for any index σ ∈ [3/2, 2], we obtain the local in time well-posedness in the space of Gevrey class G in the tangential variable and Sobolev class in the normal variable so that the monotonicity condition on the tangential velocity is not needed to overcome the loss of tangential derivative. This answers the open question raised in the paper of D. Gérard-Varet and N. Masmoudi [Ann. Sci. Éc. Norm. Supér. (4) 48 (2015), no. 6, 1273-1325], in which the case σ = 7/4 is solved. |
| Starting Page | 717 |
| Ending Page | 775 |
| Page Count | 59 |
| File Format | PDF HTM / HTML |
| DOI | 10.4171/jems/931 |
| Volume Number | 22 |
| Alternate Webpage(s) | http://arxiv-export-lb.library.cornell.edu/pdf/1609.08430 |
| Alternate Webpage(s) | https://doi.org/10.4171/jems%2F931 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
