Well-Posedness of Stochastic Mean-Field Schrödinger Porous-Medium Equations and Control of Their Modal Reductions
Abstract
We investigate stochastic mean-field Schrödinger-type equations driven by complex-valued porousmedium operators, with nonhomogeneous random Dirichlet boundary conditions and law dependence in both drift and diffusion coefficients. We prove existence and uniqueness of strong solutions by combining a lifting of the random boundary datum, monotonicity methods, Galerkin approximations, and a fixed-point argument for the associated measure flow. This extends existing well-posedness results by allowing a law-dependent diffusion coefficient and random nonhomogeneous boundary data. We also prove exact controllability for a class of finite-dimensional linear mean-field stochastic differential equations with possibly degenerate diffusion controls. The result relies on a Gramian condition for the mean dynamics and a range-inclusion condition compensating for the degenerate directions. Modal reductions of linear stochastic Schrödinger-type equations illustrate the connection between the two settings.
Related
- Correction to the article "Global well-posedness and scattering in weighted space for nonlinear Schrödinger equations below the Strauss exponent without gauge-invariance"
- A sharp criterion for well-posedness of semilinear Schrödinger equations on the real line
- Global well-posedness and scattering for energy-critical Schrodinger equations with conservative Marcus noise
- Fully fractional Schrödinger equations with memory: well-posedness via extension
- Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions
BibTeX
@misc{brehuescu2026wellposedness,
title = {{Well-Posedness of Stochastic Mean-Field Schrödinger Porous-Medium Equations and Control of Their Modal Reductions}},
author = {Gabriel Brehuescu and Dan Goreac},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://univ-eiffel.hal.science/hal-05795670v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Well-Posedness of Stochastic Mean-Field Schrödinger Porous-Medium Equations and Control of Their Modal Reductions
AU - Gabriel Brehuescu
AU - Dan Goreac
PY - 2026
DA - 2026/09/01
PB - HAL
UR - https://univ-eiffel.hal.science/hal-05795670v1
AB - We investigate stochastic mean-field Schrödinger-type equations driven by complex-valued porousmedium operators, with nonhomogeneous random Dirichlet boundary conditions and law dependence in both drift and diffusion coefficients. We prove existence and uniqueness of strong solutions by combining a lifting of the random boundary datum, monotonicity methods, Galerkin approximations, and a fixed-point argument for the associated measure flow. This extends existing well-posedness results by allowing a law-dependent diffusion coefficient and random nonhomogeneous boundary data. We also prove exact controllability for a class of finite-dimensional linear mean-field stochastic differential equations with possibly degenerate diffusion controls. The result relies on a Gramian condition for the mean dynamics and a range-inclusion condition compensating for the degenerate directions. Modal reductions of linear stochastic Schrödinger-type equations illustrate the connection between the two settings.
ER -