73 citations · 269 across the 22 of their papers we have counts for
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Ergodic results for the stochastic nonlinear Schrödinger equation with large damping
Zdzislaw Brzezniak, Benedetta Ferrario, Margherita Zanella
We study the nonlinear Schrödinger equation with linear damping, i.e. a zero order dissipation, and additive noise. Working in with d = 2 or d = 3, we prove the uniqueness of…
On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach
Zdzislaw Brzezniak, Gabriel Deugoue, Paul Andre Razafimandimby
In this manuscript, we consider a highly nonlinear and constrained stochastic PDEs modelling the dynamics of 2-dimensional nematic liquid crystals under random perturbation. This s…
3D Stochastic Landau-Lifshitz-Gilbert Equations coupled with Maxwell's Equations with full energy
Zdzislaw Brzezniak, Ben Goldys, Liang Li
We consider 3D stochastic Landau-Lifshitz-Gilbert equations coupled with the Maxwell equations with the full energy. We have proved the existence and some further regularities of t…
Stochastic Navier-Stokes equations on a thin spherical domain
Zdzisław Brzeźniak, Gaurav Dhariwal, Quoc Thong Le Gia
Incompressible Navier-Stokes equations on a thin spherical domain along with free boundary conditions under a random forcing are considered. The convergence of the…
Well-posedness and large deviations for 2-D Stochastic Navier-Stokes equations with jumps
Zdzislaw Brzezniak, Xuhui Peng, Jianliang Zhai
The aim of this paper is threefold. Firstly, we prove the existence and the uniqueness of a global strong (in both the probabilistic and the PDE senses) -valued s…
Maximal inequalities and exponential estimates for stochastic convolutions driven by Lévy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations
Jiahui Zhu, Zdzisław Brzeźniak, Wei Liu
We present remarkably simple proofs of Burkholder-Davis-Gundy inequalities for stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by…