Well-Posedness of the Dispersion-Generalized Modified Benjamin-Ono Equation in Generalized Fourier-Lebesgue Spaces

Abstract

We consider the Cauchy problem of the dispersion-generalized modified Benjamin-Ono equation on the real line with low-regularity initial data. To this motivation, we apply a generalized Fourier-Lebesgue space , which serves as a unification of modulation spaces and Fourier-Lebesgue spaces. One of the key ingredients is an improved bilinear estimate and the well-posedness is obtained by perturbation arguments.