Stéphane Vento

most citedWell-posedness and ill-posedness results for dissipative Benjamin-Ono equations

10 citations · 14 across the 4 of their papers we have counts for

collaborators

4 papers

math.AP2008

Well-posedness for the generalized Benjamin-Ono equations with arbitrary large initial data in the critical space

Stéphane Vento

We prove that the generalized Benjamin-Ono equations $\partial_{t} u + H \partial_{x}^{2} u \pm u^{k} \partial_{x} u = 0$ , $k \geq 4$ are locally well-posed in the scaling invariant spaces $\…

math.AP2008★ 10 cited

Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations

Stéphane Vento

We study the Cauchy problem for the dissipative Benjamin-Ono equations $u_{t} + u ˝_{xx} + ∣ D ∣^{α} u + u u_{x} = 0$ with $0 \leq α \leq 2$ . When $0 \leq α < 1$ , we show the ill-posedness in $H^{s} (R)$ ,…

math.AP2008★ 2 cited

Asymptotic behavior for dissipative Korteweg-de Vrie equations

Stéphane Vento

We study the large time behavior of solutions to the dissipative Korteweg-de Vrie equations $u_{t} + u_{xxx} + ∣ D ∣^{α} u + u u_{x} = 0$ with $0 < α < 2$ . We find $v$ such that $u - v$ decays like $t^{-r…

math.AP2007★ 2 cited

Global well-posedness for dissipative Korteweg-de Vries equations

Stéphane Vento

This paper is devoted to the well-posedness for dissipative KdV equations $u_{t} + u_{xxx} + ∣ D_{x} ∣^{2 α} u + u u_{x} = 0$ , $0 < α \leq 1$ . An optimal bilinear estimate is obtained in Bourgain's type…