TY - JOUR
T1 - Dispersive estimates for 2D-wave equations with critical potentials
AU - Fanelli, Luca
AU - Zhang, Junyong
AU - Zheng, Jiqiang
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/5/14
Y1 - 2022/5/14
N2 - We study the 2D-wave equation with a scaling-critical electromagnetic potential. This problem is doubly critical, because of the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In particular, the diamagnetic phenomenon allows to consider negative electric potential which can be singular in the same fashion as the inverse-square potential. We prove sharp time-decay estimates in the purely magnetic case, and Strichartz estimates for the complete model, involving a critical electromagnetic field.
AB - We study the 2D-wave equation with a scaling-critical electromagnetic potential. This problem is doubly critical, because of the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In particular, the diamagnetic phenomenon allows to consider negative electric potential which can be singular in the same fashion as the inverse-square potential. We prove sharp time-decay estimates in the purely magnetic case, and Strichartz estimates for the complete model, involving a critical electromagnetic field.
KW - Aharonov-Bohm magnetic field
KW - Decay estimates
KW - Scaling-critical electromagnetic potential
KW - Strichartz estimates
KW - Wave equation
UR - http://www.scopus.com/inward/record.url?scp=85126532758&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2022.108333
DO - 10.1016/j.aim.2022.108333
M3 - Article
AN - SCOPUS:85126532758
SN - 0001-8708
VL - 400
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 108333
ER -