TY - JOUR
T1 - On the boundary Strichartz estimates for wave and Schrödinger equations
AU - Guo, Zihua
AU - Li, Ji
AU - Nakanishi, Kenji
AU - Yan, Lixin
PY - 2018/12/5
Y1 - 2018/12/5
N2 - We consider the Lt
2Lx
r estimates for the solutions to the wave and Schrödinger equations in high dimensions. For the homogeneous estimates, we show Lt
2Lx
∞ estimates fail at the critical regularity in high dimensions by using stable Lévy process in Rd. Moreover, we show that some spherically averaged Lt
2Lx
∞ estimate holds at the critical regularity. As a by-product we obtain Strichartz estimates with angular smoothing effect. For the inhomogeneous estimates, we prove double Lt
2-type estimates.
AB - We consider the Lt
2Lx
r estimates for the solutions to the wave and Schrödinger equations in high dimensions. For the homogeneous estimates, we show Lt
2Lx
∞ estimates fail at the critical regularity in high dimensions by using stable Lévy process in Rd. Moreover, we show that some spherically averaged Lt
2Lx
∞ estimate holds at the critical regularity. As a by-product we obtain Strichartz estimates with angular smoothing effect. For the inhomogeneous estimates, we prove double Lt
2-type estimates.
KW - Nonlinear Schrödinger equation
KW - Nonlinear wave equation
KW - Strichartz estimates
UR - http://www.scopus.com/inward/record.url?scp=85049643313&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2018.07.010
DO - 10.1016/j.jde.2018.07.010
M3 - Article
AN - SCOPUS:85049643313
SN - 0022-0396
VL - 265
SP - 5656
EP - 5675
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 11
ER -