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

Authors

Zijun Chen School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China https://orcid.org/0009-0000-4100-8058
Chunyan Huang School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, China https://orcid.org/0000-0002-2535-6033

DOI:

https://doi.org/10.37256/cm.6320256615

Keywords:

dispersion-generalized modified Benjamin-Ono equations, local well-posedness, modulation spaces, 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.