2018年12月
On the boundary Strichartz estimates for wave and Schrödinger equations
J. Differential Equations
- ,
- ,
- ,
- 巻
- 265
- 号
- 11
- 開始ページ
- 5656
- 終了ページ
- 5675
- 記述言語
- 英語
- 掲載種別
- 研究論文（学術雑誌）
We consider the $L_t^2L_x^r$ estimates for the solutions to the wave and<br />
Schr\"odinger equations in high dimensions. For the homogeneous estimates, we<br />
show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high<br />
dimensions by using stable L\'evy process in $\R^d$. Moreover, we show that<br />
some spherically averaged $L_t^2L_x^\infty$ estimate holds at the critical<br />
regularity. As a by-product we obtain Strichartz estimates with angular<br />
smoothing effect. For the inhomogeneous estimates, we prove double $L_t^2$-type<br />
estimates.
Schr\"odinger equations in high dimensions. For the homogeneous estimates, we<br />
show $L_t^2L_x^\infty$ estimates fail at the critical regularity in high<br />
dimensions by using stable L\'evy process in $\R^d$. Moreover, we show that<br />
some spherically averaged $L_t^2L_x^\infty$ estimate holds at the critical<br />
regularity. As a by-product we obtain Strichartz estimates with angular<br />
smoothing effect. For the inhomogeneous estimates, we prove double $L_t^2$-type<br />
estimates.
- ID情報
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- arXiv ID : arXiv:1805.01180