Well-posedness in energy space for the periodic modified Benjamin-Ono equation

Abstract

We prove that the periodic modified Benjamin-Ono equation is locally well-posed in the energy space $H^{1/2}$. This ensures the global well-posedness in the defocusing case. The proof is based on an $X^{s,b}$ analysis of the system after gauge transform.

26 pages, 0 figure. Title changed, introduction modified

References in corpus (1)

• Local well-posedness and blow up in the energy space for a class of L2 critical dispersion generalized Benjamin-Ono equations