Local Well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces
| dc.creator | Guo, Zihua | |
| dc.date | 2008-12-10 | |
| dc.date | 2008-12-21 | |
| dc.date.accessioned | 2026-07-07T12:20:41Z | |
| dc.date.available | 2026-07-07T12:20:41Z | |
| dc.description | We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation \[\partial_t u+|\partial_x|^{1+α}\partial_x u+uu_x=0,\ u(x,0)=u_0(x),\] is locally well-posed in the Sobolev spaces $H^s$ for $s>1-α$ if $0\leq α\leq 1$. The new ingredient is that we develop the methods of Ionescu, Kenig and Tataru \cite{IKT} to approach the problem in a less perturbative way, in spite of the ill-posedness results of Molinet, Saut and Tzvetkovin \cite{MST}. Moreover, as a bi-product we prove that if $0<α\leq 1$ the corresponding modified equation (with the nonlinearity $\pm uuu_x$) is locally well-posed in $H^s$ for $s\geq 1/2-α/4$. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/0812.1825 | |
| dc.identifier | http://arxiv.org/abs/0812.1825 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213132 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q53 | |
| dc.title | Local Well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces | |
| dc.type | text |