Electron. J. Diff. Equ., Vol. 2012 (2012), No. 40, pp. 1-15.

Well-posedness of KdV type equations

Xavier Carvajal, Mahendra Panthee

In this work, we study the initial value problems associated to some linear perturbations of KdV equations. Our focus is in the well-posedness issues for 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 space associated to the KdV equation. With this method, we can use the multilinear estimates developed in the KdV context, thereby getting analogous well-posedness results for linearly perturbed equations.

Submitted September 9, 2011. Published March 14, 2012.
Math Subject Classifications: 35A07, 35Q53.
Key Words: Initial value problem; well-posedness; Bourgain spaces, KdV equation.

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Xavier Carvajal
Instituto de Matemática - UFRJ Av. Horácio Macedo
Centro de Tecnologia Cidade Universitária, Ilha do Fundão
Caixa Postal 68530, 21941-972 Rio de Janeiro, RJ, Brasil
email: carvajal@im.ufrj.br
Mahendra Panthee
Centro de Matemática
Universidade do Minho
4710-057, Braga, Portugal
email: mpanthee@math.uminho.pt

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