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arXiv · 2608.27846

Strichartz estimates to fractional Schrödinger equations

Jie Chen·Yiran Gong·Ying Zhang
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Abstract

In this paper, we firstly study Strichartz estimates $\|e^{it D^α} u_0\|_{L_t^q(\mathbb{R};L_x^r(\mathbb{R}^d))}\leq C(d,α,q,r,s)\|u_0\|_{\dot{H}^s}.$ We show some counterexamples for $(q,r) = (2,\infty)$. Then we consider the embedding $X^{s,b}_α\hookrightarrow L_t^q(\mathbb{R};L_x^r(\mathbb{R}^d))$, where $\|u\|_{X_α^{s,b}}:=\|\langleξ\rangle^s\langle τ-|ξ|^α\rangle^b\hat{u}(τ,ξ)\|_{L^2_{τ,ξ}}$. We present the necessary and sufficient conditions for this embedding.

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Jie Chen, Yiran Gong, Ying Zhang. 2026-08-28. Strichartz estimates to fractional Schrödinger equations. https://arxiv.org/abs/2608.27846

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