Add to ORKGInternational audienceWe prove that the KdV-Burgers is globally well-posed in $ H^{-1}(\T) $ with a solution-map that is analytic from $H^{-1}(\T) $ to $C([0,T];H^{-1}(\T))$ whereas it is ill-posed in $ H^s(\T) $, as soon as $ s0 $ small enough. In view of the result of Kappeler and Topalov for KdV it thus appears that even if the dissipation part of the KdV-Burgers equation allows to lower the $ C^\infty $ critical index with respect to the KdV equation, it does not permit to improve the $ C^0$ critical index
In this work, we study the initial value problems associated to some linear perturbations of the KdV...
Given smooth step-like initial data $V(0,x)$ on the real line, we show that the Korteweg--de Vries e...
We establish local well-posedness in Sobolev spaces $H^s(\mathbb{T})$, with $s\geq -1/2$, for the in...
International audienceWe prove that the KdV-Burgers is globally well-posed in $ H^{-1}(\T) $ with a ...
International audienceWe complete the known results on the local Cauchy problem in Sobolev spaces fo...
International audienceWe prove local and global well-posedness in $H^{s,0}(\mathbb{R}^{2})$, $s > -\...
We consider higher order viscous Burgers' equations with generalized nonlinearity and study the asso...
International audienceWe establish a new a priori bound for $ L^2 $-bounded sequences of solutions t...
International audienceNonlocal generalizations of Burgers equation were derived in earlier work by H...
International audienceNonlocal generalizations of Burgers equation were derived in earlier work by H...
AbstractWe establish a new a priori bound for L2-bounded sequences of solutions to the mKdV equation...
ill-posedness and well-posedness results for the KdV-Burgers equation: the periodic cas
In this paper, we study the Ostrovsky, Stepanyams and Tsimring equation. We show that the associated...
International audienceWe prove that the solution-map $ u_0 \mapsto u $ associated with the KdV equat...
We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), ...
In this work, we study the initial value problems associated to some linear perturbations of the KdV...
Given smooth step-like initial data $V(0,x)$ on the real line, we show that the Korteweg--de Vries e...
We establish local well-posedness in Sobolev spaces $H^s(\mathbb{T})$, with $s\geq -1/2$, for the in...
International audienceWe prove that the KdV-Burgers is globally well-posed in $ H^{-1}(\T) $ with a ...
International audienceWe complete the known results on the local Cauchy problem in Sobolev spaces fo...
International audienceWe prove local and global well-posedness in $H^{s,0}(\mathbb{R}^{2})$, $s > -\...
We consider higher order viscous Burgers' equations with generalized nonlinearity and study the asso...
International audienceWe establish a new a priori bound for $ L^2 $-bounded sequences of solutions t...
International audienceNonlocal generalizations of Burgers equation were derived in earlier work by H...
International audienceNonlocal generalizations of Burgers equation were derived in earlier work by H...
AbstractWe establish a new a priori bound for L2-bounded sequences of solutions to the mKdV equation...
ill-posedness and well-posedness results for the KdV-Burgers equation: the periodic cas
In this paper, we study the Ostrovsky, Stepanyams and Tsimring equation. We show that the associated...
International audienceWe prove that the solution-map $ u_0 \mapsto u $ associated with the KdV equat...
We prove that the initial value problem (IVP) for the BBM equation is ill-posed for data in Hs(R), ...
In this work, we study the initial value problems associated to some linear perturbations of the KdV...
Given smooth step-like initial data $V(0,x)$ on the real line, we show that the Korteweg--de Vries e...
We establish local well-posedness in Sobolev spaces $H^s(\mathbb{T})$, with $s\geq -1/2$, for the in...