Well-posedness results for the dispersion generalized Benjamin-Ono equation via the contraction principle

Abstract

We study the initial value problem associated to the dispersion generalized Benjamin-Ono equation. Our aim is to establish well-posedness results in weighted Sobolev spaces via contraction principle under minimal requirements in the weighted order of the space. One of our new main ideas is the deduction of a pointwise estimate concerning the group describing the solution of the linear problem and the fractional weights.

22 pages. The paper has been withdrawn due to an error in the maximal norm estimate that we haven't been able to overcome

References in corpus (4)

• Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations
• A para-differential renormalization technique for nonlinear dispersive equations
• The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces
• Nonlinear wave interactions for the Benjamin-Ono equation

Cited by in corpus (1)

• The Cauchy problem for a fifth order KdV equation in weighted Sobolev spaces