On a priori estimates and existence of periodic solutions to the modified Benjamin-Ono equation below <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-struck">T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>
نویسندگان
چکیده
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 time. The approach relies on frequency dependent time localization, after which dispersive properties from Euclidean space recovered. same regularity results cubic derivative nonlinear Schr\"odinger equation.
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2021
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2021.07.019