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 -