TY - JOUR
T1 - On 1d Quadratic Klein–Gordon Equations with a Potential and Symmetries
AU - Germain, Pierre
AU - Pusateri, Fabio
AU - Zhang, Katherine Zhiyuan
N1 - Funding Information:
While working on this project, PG was supported by the NSF Grant DMS-1501019, by the Simons collaborative grant on weak turbulence, by the Center for Stability, Instability and Turbulence (NYUAD), and by the Erwin Schrödinger Institute. FP was supported in part by a start-up Grant from the University of Toronto, NSERC Grant No. 06487, and a Connaught Foundation New Researcher Award. ZZ was supported by the Simons collaborative Grant on weak turbulence and by an AMS-Simons travel Grant.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.
PY - 2023/4
Y1 - 2023/4
N2 - This paper is a continuation of the previous work (Pusateri, in: Forum of mathematics, Cambridge University Press) by the first two authors. We focus on 1-dimensional quadratic Klein–Gordon equations with a potential, under some assumptions that are less general than (Pusateri, in: Forum of mathematics, Cambridge University Press), but that allow us to present some simplifications in the proof of the global existence with decay for small solutions. In particular, we can propagate a stronger control on a basic L2-weighted-type norm while providing some shorter and less technical proofs for some of the arguments.
AB - This paper is a continuation of the previous work (Pusateri, in: Forum of mathematics, Cambridge University Press) by the first two authors. We focus on 1-dimensional quadratic Klein–Gordon equations with a potential, under some assumptions that are less general than (Pusateri, in: Forum of mathematics, Cambridge University Press), but that allow us to present some simplifications in the proof of the global existence with decay for small solutions. In particular, we can propagate a stronger control on a basic L2-weighted-type norm while providing some shorter and less technical proofs for some of the arguments.
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U2 - 10.1007/s00205-023-01853-0
DO - 10.1007/s00205-023-01853-0
M3 - Article
AN - SCOPUS:85149329987
SN - 0003-9527
VL - 247
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
M1 - 17
ER -