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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.18035 |
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| _version_ | 1866915462058606592 |
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| author | Chen, Jie Gu, Fan Guo, Boling |
| author_facet | Chen, Jie Gu, Fan Guo, Boling |
| contents | 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 $$\|u\|_{X^{s,b}}:=\|\hat{u}(τ,ξ)\langle ξ\rangle^s\langle τ-ξ^3\rangle^b \|_{L_{τ,ξ}^2}. $$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz type estimates of the Airy equation Chen, Jie Gu, Fan Guo, Boling Analysis of PDEs 35Q53 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 $$\|u\|_{X^{s,b}}:=\|\hat{u}(τ,ξ)\langle ξ\rangle^s\langle τ-ξ^3\rangle^b \|_{L_{τ,ξ}^2}. $$ 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. |
| title | Strichartz type estimates of the Airy equation |
| topic | Analysis of PDEs 35Q53 |
| url | https://arxiv.org/abs/2508.18035 |