Analytic-Gevrey well-posedness of generalized Benjamin-Ono equation

Abstract

Under data in analytic Gevrey spaces on the line, we show the existence of one-dimensional generalization of the Benjamin-Ono equation. We also deal the regularity in t and x, where the solution will be in G^σ in x and belongs to G^(1+α)σ near 0 in t. The proof is based on [18] and inspired from the ideas introduced in [3].

Subject Classification: (2010):

• 35E15
• 35Q53
• 35B65
• 35C07

Keywords:

• Benjamin-Ono equation
• Well-posedness
• Analytic Gevrey spaces
• Bourgain spaces
• Bilinear estimates
• Gevrey time regularity