Two dimensional nonlinear Schrödinger equation with spatial white noise potential and fourth order nonlinearity

Nikolay Tzvetkov, N. Visciglia

Type: Article

Publication Date: 2022-04-09

Citations: 6

DOI: https://doi.org/10.1007/s40072-022-00251-z

Abstract

Abstract We consider NLS on $$\mathbb {T}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> with multiplicative spatial white noise and nonlinearity between cubic and quartic. We prove global existence, uniqueness and convergence almost surely of solutions to a family of properly regularized and renormalized approximating equations. In particular we extend a previous result by A. Debussche and H. Weber available in the cubic and sub-cubic setting.

Locations

Stochastic Partial Differential Equations Analysis and Computations - View - PDF

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