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SUMMARY:Weak Martingale Solutions for the Stochastic Nonlinear Fractional 
 Schrödinger Equations - Zdzislaw Brzezniak (University of York)
DTSTART:20220214T090000Z
DTEND:20220214T100000Z
UID:TALK170015@talks.cam.ac.uk
DESCRIPTION:&nbsp\;I will speak about the existence of Weak Martingale Sol
 utions for the Stochastic Nonlinear fractional Schr&ouml\;dinger Equations
  on riemannian manifolds.&nbsp\; These results &nbsp\;are&nbsp\; special c
 ases of general results obtained jointly with Lutz Weis and Fabian Hornung
 . I will also speak about the existence of invariant measures and stationa
 ry solutions to such equations &nbsp\;obtained jointly with Benedetta Ferr
 ario and Margherita Zanella. I will conclude\, if time allows talking abou
 t the uniqueness results which so far have been proved for\nStochastic Non
 linear (non-fractional) Schr&ouml\;dinger Equations and which generalisati
 ons to Stochastic Nonlinear fractional Schr&ouml\;dinger Equations would b
 e of some interested.\nReferences:\n[1] Z. Brzezniak\, F.&nbsp\; Hornung\,
 &nbsp\; and L.&nbsp\; Weis\, Martingale solutions for the stochastic nonli
 near Schr&ouml\;dinger equation in the energy space.\n&nbsp\;Probab. Theor
 y Related Fields&nbsp\; 174\,&nbsp\; no. 3-4\, 1273--1338 (2019)\n[2] Z. B
 rzezniak\, B. Ferrario and M. Zanella\, Invariant measures for a stochasti
 c nonlinear and damped&nbsp\; 2D Schr\\"odinger equation\, arxiv\n[3] Z. B
 rzezniak\, F.&nbsp\; Hornung\,&nbsp\; and L.&nbsp\; Weis\, Uniqueness of m
 artingale solutions for the stochastic nonlinear Schr\\"odinger equation o
 n 3d compact manifolds\, to appear\n&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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