Sharp ill-posedness and well-posedness results for the KdV-Burgers equation: the periodic case

2010/05/26 by Molinet, Luc, Vento, Stéphane
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1005.4805

Abstract

We 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^∞ critical index with respect to the KdV equation, it does not permit to improve the C⁰ critical index .

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