Local well-posedness for the two-component Benjamin-Ono equation
Abstract The Cauchy problem for the two-component Benjamin-Ono equation is considered. It is shown that this problem is local well-posed in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>H</m:mi> </m:mrow> <m:mrow> <m:mi>s</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>×</m:mo> <m:msup> <m:mrow> <m:mi>H</m:mi> </m:mrow> <m:mrow> <m:mi>s</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {H}^{s}\left({\mathbb{R}})\times {H}^{s}\left({\mathbb{R}}) for any <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>s</m:mi> <m:mo>></m:mo> <m:mn>9</m:mn> <m:mo>⁄</m:mo> <m:mn>8</m:mn> </m:math> s\gt 9/8 . A local smoothing effect in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>H</m:mi> </m:mrow> <m:mrow> <m:mi>s</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>×</m:mo> <m:msup> <m:mrow> <m:mi>H</m:mi> </m:mrow> <m:mrow> <m:mi>s</m:mi> </m:mrow> </m:msup> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {H}^{s}\left({\mathbb{R}})\times {H}^{s}\left({\mathbb{R}}) , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>s</m:mi> <m:mo>></m:mo> <m:mn>3</m:mn> <m:mo>⁄</m:mo> <m:mn>2</m:mn> </m:math> s\gt 3/2 is also established.
Authors
- Min Zhao (ORCID: https://orcid.org/0000-0002-9888-4443)
Institutions
- Ningbo University of Technology (CN)
Publication Details
- Journal
- Advances in Nonlinear Analysis
- Published
- 2025-01-01
- DOI
- https://doi.org/10.1515/anona-2025-0119
- Primary Topic
- Nonlinear Waves and Solitons
- Type
- article
- Field-Weighted Citation Impact
- 0.00