TY - JOUR
T1 - Long time dynamics for semi-relativistic NLS and half wave in arbitrary dimension
AU - Bellazzini, Jacopo
AU - Georgiev, Vladimir
AU - Visciglia, Nicola
N1 - Funding Information:
V.G. is supported in part by INDAM, GNAMPA–Gruppo Nazionale per l’Analisi Matematica, la Probabilita e le loro Applicazion, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences and by Top Global University Project, Waseda University. J.B. and V.G. are supported by Gnampa 2017 project “Problemi stazionari e di evoluzioni per equazioni di campo non lineari”.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/6/1
Y1 - 2018/6/1
N2 - We consider the Cauchy problems associated with semi-relativistic NLS (sNLS) and half wave (HW). In particular we focus on the following two main questions: local/global Cauchy theory; existence and stability/instability of ground states. In between other results, we prove the existence and stability of ground states for sNLS in the L2 supercritical regime. This is in sharp contrast with the instability of ground states for the corresponding HW, which is also established along the paper, by showing an inflation of norms phenomenon. Concerning the Cauchy theory we show, under radial symmetry assumption the following results: a local existence result in H1 for energy subcritical nonlinearity and a global existence result in the L2 subcritical regime.
AB - We consider the Cauchy problems associated with semi-relativistic NLS (sNLS) and half wave (HW). In particular we focus on the following two main questions: local/global Cauchy theory; existence and stability/instability of ground states. In between other results, we prove the existence and stability of ground states for sNLS in the L2 supercritical regime. This is in sharp contrast with the instability of ground states for the corresponding HW, which is also established along the paper, by showing an inflation of norms phenomenon. Concerning the Cauchy theory we show, under radial symmetry assumption the following results: a local existence result in H1 for energy subcritical nonlinearity and a global existence result in the L2 subcritical regime.
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U2 - 10.1007/s00208-018-1666-z
DO - 10.1007/s00208-018-1666-z
M3 - Article
AN - SCOPUS:85043389723
SN - 0025-5831
VL - 371
SP - 707
EP - 740
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -