TY - JOUR
T1 - Strichartz estimates for the magnetic Schrödinger equation with potentials V of critical decay
AU - Kim, Seonghak
AU - Koh, Youngwoo
N1 - Publisher Copyright:
© 2017 Taylor & Francis.
PY - 2017/9/2
Y1 - 2017/9/2
N2 - We study the Strichartz estimates for the magnetic Schrödinger equation in dimension n≥3. More specifically, for all Schrödinger admissible pairs (r,q), we establish the estimate (Formula presented.) when the operator H = −ΔA+V satisfies suitable conditions. In the purely electric case A≡0, we extend the class of potentials V to the Fefferman–Phong class. In doing so, we apply a weighted estimate for the Schrödinger equation developed by Ruiz and Vega. Moreover, for the endpoint estimate of the magnetic case in ℝ3, we investigate an equivalence (Formula presented.) and find sufficient conditions on H and r for which the equivalence holds.
AB - We study the Strichartz estimates for the magnetic Schrödinger equation in dimension n≥3. More specifically, for all Schrödinger admissible pairs (r,q), we establish the estimate (Formula presented.) when the operator H = −ΔA+V satisfies suitable conditions. In the purely electric case A≡0, we extend the class of potentials V to the Fefferman–Phong class. In doing so, we apply a weighted estimate for the Schrödinger equation developed by Ruiz and Vega. Moreover, for the endpoint estimate of the magnetic case in ℝ3, we investigate an equivalence (Formula presented.) and find sufficient conditions on H and r for which the equivalence holds.
KW - Fefferman-Phong class
KW - Strichartz estimates
KW - magnetic Schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=85030159449&partnerID=8YFLogxK
U2 - 10.1080/03605302.2017.1377229
DO - 10.1080/03605302.2017.1377229
M3 - Article
AN - SCOPUS:85030159449
SN - 0360-5302
VL - 42
SP - 1467
EP - 1480
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 9
ER -