The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces

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 and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model.

36 pages

References in corpus (4)

• The sharp Hardy Uncertainty Principle for Schödinger evolutions
• 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

Cited by in corpus (10)

• The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces
• The Generalized Fractional Benjamin-Bona-Mahony Equation: Analytical and Numerical Results
• Enhanced existence time of solutions to the fractional Korteweg-de Vries equation
• On the propagation of regularity for solutions of the Dispersion Generalized Benjamin-Ono Equation
• On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation
• On the propagation of regularity and decay of solutions to the Benjamin equation
• Well-posedness results for the dispersion generalized Benjamin-Ono equation via the contraction principle
• The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces
• The Cauchy problem for a fifth order KdV equation in weighted Sobolev spaces
• Asymptotic behavior of solutions of the dispersive generalized Benjamin-Ono equation