Small data scattering for semi-relativistic equations with Hartree type nonlinearity

Herr S, Tesfahun A (2015)
Journal of Differential Equations 259(10): 5510-5532.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Herr, SebastianUniBi ; Tesfahun, Achenef
Abstract / Bemerkung
We prove that the initial value problem for the equation i partial derivative tu + root m2-Delta u = (e-mu broken vertical bar x broken vertical bar/broken vertical bar x broken vertical bar* broken vertical bar u broken vertical bar) u in R1+3, m >= 0, mu 0 > 0 is globally well-posed and the solution scatters to free waves asymptotically as t oo if we start with initial data which is small in FP (R3) for s> and if m > 0. Moreover, if the initial data is radially symmetric we can improve the above result to m > 0 and s > 0, which is almost optimal, in the sense that L-2(R-3) is the critical space for the equation. The main ingredients in the proof are certain endpoint Strichartz estimates, L-2(R1+3) bilinear estimates for free waves and an application of the UP and VP function spaces. (C) 2015 Elsevier Inc. All rights reserved.
Erscheinungsjahr
2015
Zeitschriftentitel
Journal of Differential Equations
Band
259
Ausgabe
10
Seite(n)
5510-5532
ISSN
0022-0396
Page URI
https://pub.uni-bielefeld.de/record/2777691

Zitieren

Herr S, Tesfahun A. Small data scattering for semi-relativistic equations with Hartree type nonlinearity. Journal of Differential Equations. 2015;259(10):5510-5532.
Herr, S., & Tesfahun, A. (2015). Small data scattering for semi-relativistic equations with Hartree type nonlinearity. Journal of Differential Equations, 259(10), 5510-5532. doi:10.1016/j.jde.2015.06.037
Herr, S., and Tesfahun, A. (2015). Small data scattering for semi-relativistic equations with Hartree type nonlinearity. Journal of Differential Equations 259, 5510-5532.
Herr, S., & Tesfahun, A., 2015. Small data scattering for semi-relativistic equations with Hartree type nonlinearity. Journal of Differential Equations, 259(10), p 5510-5532.
S. Herr and A. Tesfahun, “Small data scattering for semi-relativistic equations with Hartree type nonlinearity”, Journal of Differential Equations, vol. 259, 2015, pp. 5510-5532.
Herr, S., Tesfahun, A.: Small data scattering for semi-relativistic equations with Hartree type nonlinearity. Journal of Differential Equations. 259, 5510-5532 (2015).
Herr, Sebastian, and Tesfahun, Achenef. “Small data scattering for semi-relativistic equations with Hartree type nonlinearity”. Journal of Differential Equations 259.10 (2015): 5510-5532.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Quellen

arXiv: 1412.1626

Suchen in

Google Scholar