Bilinear local smoothing estimate for Airy equation
Soonsik Kwon, Tristan Roy
TL;DR
This paper refines bilinear local smoothing estimates for Airy equation solutions with separated frequency supports and demonstrates a smoothing property of a related bilinear form.
Contribution
It introduces a refined bilinear local smoothing estimate for Airy solutions with separated frequencies and establishes a new smoothing property of a bilinear form.
Findings
Refined bilinear local smoothing estimate for Airy solutions
Proved smoothing property of a bilinear form
Applicable when frequency supports are separated
Abstract
In this short note, we prove a refinement of bilinear local smoothing estimate to Airy solutions, when the frequency support of two wave are separated. As an application we prove a smoothing property of a bilinear form.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Advanced Harmonic Analysis Research