TY - JOUR
T1 - Strichartz estimates for wave equation with inverse square potential
AU - Miao, Changxing
AU - Zhang, Junyong
AU - Zheng, Jiqiang
PY - 2013/12
Y1 - 2013/12
N2 - In this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional angular regularity, especially the radial initial data, the range of admissible pairs is improved. As an application, we show the global well-posedness of the semi-linear wave equation with inverse-square potential δt2u-Δu+x2/ au+±up-1u for power p being in some regime when the initial data are radial. This result extends the well-posedness result in Planchon, Stalker, and Tahvildar-Zadeh.
AB - In this paper, we study the Strichartz-type estimates of the solution for the linear wave equation with inverse square potential. Assuming the initial data possesses additional angular regularity, especially the radial initial data, the range of admissible pairs is improved. As an application, we show the global well-posedness of the semi-linear wave equation with inverse-square potential δt2u-Δu+x2/ au+±up-1u for power p being in some regime when the initial data are radial. This result extends the well-posedness result in Planchon, Stalker, and Tahvildar-Zadeh.
KW - Inverse square potential
KW - Spherical harmonics
KW - Strichartz estimate
UR - http://www.scopus.com/inward/record.url?scp=84884525932&partnerID=8YFLogxK
U2 - 10.1142/S0219199713500260
DO - 10.1142/S0219199713500260
M3 - Article
AN - SCOPUS:84884525932
SN - 0219-1997
VL - 15
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
IS - 6
M1 - 1350026-1
ER -