The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds

Herr S (2013)
American Journal of Mathematics 135(5): 1271-1290.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Let (M, g) be a three-dimensional smooth compact Riemannian manifold such that all geodesics are simple and closed with a common minimal period, such as the 3-sphere S-3 with canonical metric. In this work the global well-posedness problem for the quintic nonlinear Schrodinger equation i partial derivative(t)u + Delta u = +/-vertical bar u vertical bar(4)u, u vertical bar(t=0) = u(0) is solved for small initial data u(0) in the energy space H-1(M), which is the scaling-critical space. Further, local well-posedness for large data, as well as persistence of higher initial Sobolev regularity is obtained. This extends previous results of Burq-Gerard-Tzvetkov to the endpoint case.
Erscheinungsjahr
2013
Zeitschriftentitel
American Journal of Mathematics
Band
135
Ausgabe
5
Seite(n)
1271-1290
ISSN
0002-9327
Page URI
https://pub.uni-bielefeld.de/record/2635819

Zitieren

Herr S. The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds. American Journal of Mathematics. 2013;135(5):1271-1290.
Herr, S. (2013). The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds. American Journal of Mathematics, 135(5), 1271-1290. doi:10.1353/ajm.2013.0040
Herr, S. (2013). The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds. American Journal of Mathematics 135, 1271-1290.
Herr, S., 2013. The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds. American Journal of Mathematics, 135(5), p 1271-1290.
S. Herr, “The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds”, American Journal of Mathematics, vol. 135, 2013, pp. 1271-1290.
Herr, S.: The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds. American Journal of Mathematics. 135, 1271-1290 (2013).
Herr, Sebastian. “The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds”. American Journal of Mathematics 135.5 (2013): 1271-1290.

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