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November/December 2011 Local well-posedness and a priori bounds for the modified Benjamin-Ono equation
Zihua Guo
Adv. Differential Equations 16(11/12): 1087-1137 (November/December 2011).

Abstract

We prove that the complex-valued modified Benjamin-Ono (mBO) equation is analytically locally well posed if the initial data $\phi$ belongs to $H^s$ for $s\geq 1/2$ with $ \| {\phi} \| _{L^2}$ sufficiently small, without performing a gauge transformation. The key ingredient is that the logarithmic divergence in the high-low frequency interaction can be overcome by a combination of $X^{s,b}$ structure and smoothing effect structure. We also prove that the real-valued $H^\infty$ solutions to the mBO equation satisfy a priori local-in-time $H^s$ bounds in terms of the $H^s$ size of the initial data for $s>1/4$.

Citation

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Zihua Guo. "Local well-posedness and a priori bounds for the modified Benjamin-Ono equation." Adv. Differential Equations 16 (11/12) 1087 - 1137, November/December 2011.

Information

Published: November/December 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1236.35121
MathSciNet: MR2858525

Subjects:
Primary: 35Q35, 35Q53

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.16 • No. 11/12 • November/December 2011
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