Sharp Local Well-posedness Of Kdv Type Equations With Dissipative Pertubations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In this work, we study the initial value problems associated to some linear perturbations of the KdV equation. Our focus is on the well-posedness issues for initial data given in the L-2-based Sobolev spaces. We derive a bilinear estimate in a space with weight in the time variable and obtain sharp local well-posedness results.743571594CNPq [304036/2014-5, 481715/2012-6, 479558/2013-2, 305483/2014-5]FAPESP [2012/20966-4]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP