Unconditional uniqueness for the periodic modified Benjamin-Ono equation by normal form approach

2019/12/03 by Kishimoto, Nobu
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.01363

Abstract

We show that the solution (in the sense of distribution) to the Cauchy problem with the periodic boundary condition associated with the modified Benjamin-Ono equation is unique in L^∞_t(H^s(\mathbbT)) for s>1/2. The proof is based on the analysis of a normal form equation obtained by infinitely many reduction steps using integration by parts in time after a suitable gauge transform.

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