Local well-posedness for the modified KdV equation in almost critical ^H^r_s-spaces
| dc.creator | Gruenrock, Axel | |
| dc.creator | Vega, Luis | |
| dc.date | 2007-03-01 | |
| dc.date.accessioned | 2026-07-07T07:49:35Z | |
| dc.date.available | 2026-07-07T07:49:35Z | |
| dc.description | We study the Cauchy problem for the modified KdV equation for data u_0 in the space ^H^r_s defined by the norm ||u_0||_{^H^r_s}:=||<ξ>^s u^_0||_{L^r'_ξ}. Local well-posedness of this problem is established in the parameter range 2>=r>1, s>=1/2-1/2r, so the case (s,r)=(0,1), which is critical in view of scaling considerations is almost reached. To show this result, we use an appropriate variant of the Fourier restriction norm method as well as bi- and trilinear estimates for solutions of the Airy equation. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703037 | |
| dc.identifier | http://arxiv.org/abs/math/0703037 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124908 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53 | |
| dc.title | Local well-posedness for the modified KdV equation in almost critical ^H^r_s-spaces | |
| dc.type | text |