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

1 LMAM
LMAM - School of Mathematical Sciences
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.
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https://hal.archives-ouvertes.fr/hal-01206024
Contributor : Luc Molinet <>
Submitted on : Monday, September 28, 2015 - 12:29:53 PM
Last modification on : Thursday, March 5, 2020 - 5:33:30 PM
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• HAL Id : hal-01206024, version 1

### Citation

Zihua Guo, Yiquan Lin, Luc Molinet. Well-posedness in energy space for the periodic modified Benjamin-Ono equation. Journal of Differential Equations, Elsevier, 2014, 256 (8), pp.2778-2806. ⟨hal-01206024⟩

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