Electronic Journal of Probability

The Schrödinger equation with spatial white noise potential

Arnaud Debussche and Hendrik Weber

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We consider the linear and nonlinear Schrödinger equation with a spatial white noise as a potential over the two dimensional torus. We prove existence and uniqueness of solutions to an initial value problem for suitable initial data. Our construction is based on a change of unknown originally used in [13] and conserved quantities.

Article information

Electron. J. Probab., Volume 23 (2018), paper no. 28, 16 pp.

Received: 12 December 2016
Accepted: 16 January 2018
First available in Project Euclid: 30 March 2018

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

nonlinear Schrödinger equation spatial white noise renormalization

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Debussche, Arnaud; Weber, Hendrik. The Schrödinger equation with spatial white noise potential. Electron. J. Probab. 23 (2018), paper no. 28, 16 pp. doi:10.1214/18-EJP143. https://projecteuclid.org/euclid.ejp/1522375268

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