Laboratoire d’Analyse et de Mathématiques Appliquées

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most citedA reduced-order strategy for 4D-Var data assimilation

57 citations

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9 papers · 1 filter

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★ 3 cited

The Leray and Fujita-Kato theorems for the Boussinesq system with partial viscosity

R. Danchin, M. Paicu

We are concerned with the so-called Boussinesq equations with partial viscosity. These equations consist of the ordinary incompressible Navier-Stokes equations with a forcing term…

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…

math.AP2004

Bubble towers for supercritical semilinear elliptic equations

Yuxin Ge, Ruihua Jing, Frank Pacard

We construct positive solutions of the semilinear elliptic problem $Δ u + λ u + u^{p} = 0$ with Dirichet boundary conditions, in a bounded smooth domain $Ω \subset R^{N}$ $(N \geq 4)$ , whe…