Wednesday, July 12, 2023 - 14:00 in ZiF
Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space
A talk in the SPDEs, optimal control and mean field games series by
Arnaud Debussche from Rennes
| Abstract: |
We consider the nonlinear Schrödinger equation with multiplicative spatial white
noise and an arbitrary polynomial nonlinearity on the two-dimensional full space
domain. We prove global well-posedness by using a gauge-transform introduced
by Hairer and Labbè (2015) and constructing the solution as a limit of solutions
to a family of approximating equations. This paper extends a previous result
by Debussche and Martin (2019) with a sub-quadratic nonlinearity.
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