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arXiv · 2508.18035

Strichartz type estimates of the Airy equation

Jie Chen·Fan Gu·Boling Guo
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Abstract

In this article, we show the necessary and sufficient conditions for the inequality $\|u\|_{L_t^qL_x^r}\lesssim \|u\|_{X^{s,b}}$, where $$\|u\|_{X^{s,b}}:=\|\hat{u}(\tau,\xi)\langle \xi\rangle^s\langle \tau-\xi^3\rangle^b \|_{L_{\tau,\xi}^2}. $$ Here, we provide a complete classification of the indices relationships for which this inequality holds true. Such estimates will be very useful in solving the well-posedness for low regularity well-posedness of the Korteweg--de Vries equations and stochastic Korteweg--de Vries equations.

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Jie Chen, Fan Gu, Boling Guo. 2025-08-25. Strichartz type estimates of the Airy equation. https://arxiv.org/abs/2508.18035

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