Well-posedness of KdV type equations

Electronic Journal of Differential Equations

关键词: Initial value problem;    well-posedness;    Bourgain spaces,;    KdV equation;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this work, we study the initial value problems associated to some linearperturbations of KdV equations. Our focus is in the well-posedness issuesfor initial data given in the L^2-based Sobolev spaces.We develop a method that allows us to treat the problem in the Bourgain's spaceassociated to the KdV equation. With this method, we can use the multilinearestimates developed in the KdV context, thereby getting analogous well-posednessresults for linearly perturbed equations.

【 授权许可】

Unknown