On a priori estimates and existence of periodic solutions to the modified Benjamin-Ono equation below $H^{1/2}(\mathbb{T})$

Abstract

A priori estimates and existence of real-valued periodic solutions to the modified Benjamin-Ono equation with initial data in $H^s$ for $s>1/4$ are proved locally in time. The approach relies on frequency dependent time localization, after which dispersive properties from Euclidean space are recovered. The same regularity results are proved for the cubic derivative nonlinear Schrödinger equation.

35 pages, function spaces changed, proofs streamlined, more details for the energy estimates are provided, small L^2-norm condition for initial data could be removed

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Cited by in corpus (3)

• A priori estimates for the derivative nonlinear Schrödinger equation
• Low regularity well-posedness for generalized Benjamin-Ono equations on the circle
• Unconditional uniqueness for the periodic modified Benjamin-Ono equation by normal form approach