PreprintarXiv licencearXiv
Strichartz estimates to fractional Schrödinger equations
Abstract
In this paper, we firstly study Strichartz estimates |eit Dα u0|Ltq(ℝ;Lxr(ℝd))≤ C(d,α,q,r,s)|u0|Ḣs. We show some counterexamples for (q,r) = (2,∞). Then we consider the embedding Xs,bα↪ Ltq(ℝ;Lxr(ℝd)), where |u|Xαs,b:=|⟨ξ⟩s⟨ τ−|ξ|α⟩bû(τ,ξ)|L2τ,ξ. We present the necessary and sufficient conditions for this embedding.
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BibTeX
@misc{chen2026strichartz,
title = {{Strichartz estimates to fractional Schrödinger equations}},
author = {Jie Chen and Yiran Gong and Ying Zhang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27846},
eprint = {2608.27846},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27846},
}
RIS
TY - UNPB
TI - Strichartz estimates to fractional Schrödinger equations
AU - Jie Chen
AU - Yiran Gong
AU - Ying Zhang
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27846
UR - https://arxiv.org/abs/2608.27846
AB - In this paper, we firstly study Strichartz estimates |e^it D^α u_0|_L_t^q(ℝ;L_x^r(ℝ^d))≤ C(d,α,q,r,s)|u_0|_Ḣ^s. We show some counterexamples for (q,r) = (2,∞). Then we consider the embedding X^s,b_α↪ L_t^q(ℝ;L_x^r(ℝ^d)), where |u|_X_α^s,b:=|⟨ξ⟩^s⟨ τ−|ξ|^α⟩^bû(τ,ξ)|_L^2_τ,ξ. We present the necessary and sufficient conditions for this embedding.
ER -