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arXiv · 2306.13311

On profile decomposition for Airy type equation

Boning Di·Chenjie Fan·Dunyan Yan
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Abstract

We study the linear profile decomposition for the Airy type equation, where the associated Strichartz inequality corresponds to the Fourier extension inequality on the odd curve $\xi^{\ell}$. We also investigate an inhomogeneous case, modeled by the odd curve $\xi^3+\xi^5$ case. We note that, as observed by Frank and Sabin [Math. Ann., 2018], there is a two-profile phenomenon in the profile decomposition associated with odd curves.

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Boning Di, Chenjie Fan, Dunyan Yan. 2023-06-23. On profile decomposition for Airy type equation. https://doi.org/10.1016/j.jde.2025.01.016

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