Abstract
We show that a general family of Cauchy problems associated to NLS with randomized initial data is well posed locally in time. As initial data we consider the random vector which is associated to the Gibbs measure.
2010 Mathematics Subject Classification: 35Q40, 35Q55.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Burq, N., Thomann, L., Tzvetkov, N.: Long time dynamics for the one dimensional non linear Schrödinger equation, arXiv:1002.4054
Cazenave, T., Weissler, F.B.: The Cauchy problem for the critical nonlinear Schrödinger equation in H s. Nonlinear Anal. 14(10), 807–836 (1990)
Foschi, D.: Inhomogeneous Strichartz estimates. J. Hyperbol. Differ. Equat. 2(1), 1–24 (2005)
Ginibre, J., Velo, G.: On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case. J. Funct. Anal. 32(1), 1–32 (1979)
Vilela, M.C.: Inhomogeneous Strichartz estimates for the Schrödinger equation. Trans. Am. Math. Soc. 359(5), 2123–2136 (2007)
Yajima, K., Zhang, G.: Smoothing property for Schrödinger equations with potential superquadratic at infinity. Comm. Math. Phys. 221(3), 573–590 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Visciglia, N. (2013). On the Cauchy Problem for NLS with Randomized Initial Data. In: Cicognani, M., Colombini, F., Del Santo, D. (eds) Studies in Phase Space Analysis with Applications to PDEs. Progress in Nonlinear Differential Equations and Their Applications, vol 84. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4614-6348-1_17
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6348-1_17
Published:
Publisher Name: Birkhäuser, New York, NY
Print ISBN: 978-1-4614-6347-4
Online ISBN: 978-1-4614-6348-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)