Back to Search
Start Over
A nonlinear Schrodinger equation with fractional noise.
- Source :
- Transactions of the American Mathematical Society; Jun2021, Vol. 374 Issue 6, p4375-4422, 48p
- Publication Year :
- 2021
-
Abstract
- We study a stochastic Schrödinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension d ≤ 3. When the Hurst index is large enough, we prove local well-posedness of the problem using classical arguments. However, for a small Hurst index, even the interpretation of the equation needs some care. In this case, a renormalization procedure must come into the picture, leading to a Wick-type interpretation of the model. Our fixed-point argument then involves some specific regularization properties of the Schrödinger group, which allows us to cope with the strong irregularity of the solution. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 374
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 150085458
- Full Text :
- https://doi.org/10.1090/tran/8368