On shorttime bilinear Strichartz estimates and applications to improve the energy method
Robert Schippa
TL;DR
This paper introduces a refined energy method for dispersive PDEs with derivative nonlinearities on tori, utilizing a novel shorttime bilinear Strichartz estimate to enhance analytical techniques.
Contribution
The paper develops a new shorttime bilinear Strichartz estimate and integrates it into the energy method for better analysis of dispersive PDEs with derivative nonlinearities.
Findings
Improved bounds for dispersive PDE solutions on tori.
Enhanced analytical tools for derivative nonlinearities.
Potential applications to stability and well-posedness results.
Abstract
A refinement of the energy method is introduced for dispersive PDE with derivative nonlinearity posed on tori. Key ingredient is a shorttime bilinear Strichartz estimate, which is used in a known combination of perturbative and energy arguments.
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