4 citations · 7 across the 15 of their papers we have counts for
16 papers
Global well-posedness and Asymptotic analysis of a nonlinear heat equation with constraints of finite codimension
Ashish Bawalia, Zdzisław Brzeźniak, Manil T. Mohan
We prove the global existence and the uniqueness of the valued () strong solutions of a nonlinear heat equation with constraints over bounded doma…
Weak solutions of Navier-Stokes Equation with purely discontinuous Lévy Noise
Zdzisław Brzeźniak, Tomasz Kosmala, Elżbieta Motyl +1
In this paper we prove the existence of weak martingale solutions to the stochastic Navier-Stokes Equations driven by pure jump Lévy processes. Our proof consists of two parts. In…
Semigroups on generalized Sobolev spaces associated with Laplacians with applications Stochastic PDEs with singular boundary conditions
Sergio Albeverio, Zdzisław Brzeźniak, Szymon Peszat
Laplacians associated with domains with singular boundary conditions and are considered together with semigroups on generalized Sobolev spaces, they generate. Applications are give…
Inviscid Limit of the Stochastic Hyperviscous Navier-Stokes Equations and Invariant Measures for the Euler Equations in
Zdzisław Brzeźniak, Matteo Ferrari
We prove the existence and some moment estimates for an invariant measure for the two-dimensional (D) deterministic Euler equations on the unbounded domain and…
Global well posedness and ergodic results in regular Sobolev spaces for the nonlinear Schrödinger equation with multiplicative noise and arbitrary power of the nonlinearity
Zdzisław Brzeźniak, Benedetta Ferrario, Mario Maurelli +1
We consider the nonlinear Schrödinger equation on the -dimensional torus , with the nonlinearity of polynomial type . For any and $s>\fr…
Wave maps in dimension with an external forcing
Zdzisław Brzeźniak, Jacek Jendrej, Nimit Rana
This paper aims to establish the local and global well-posedness theory in , inspired by the approach of Keel and Tao [Internat. Math. Res. Notices, 1998], for the forced wave…
Large Deviation Principle of Stochastic Evolution Equations with reflection
Zdzisław Brzeźniak, Qi Li, Tusheng Zhang
In this paper, we establish a large deviation principle for stochastic evolution equations with reflection in an infinite dimensional ball. Weak convergence approach plays an impor…
The Ebin-Marsden toolbox for stochastic PDEs: stochastic Euler equations
Zdzisław Brzeźniak, Mario Maurelli, Alexander Schmeding
The Ebin-Marsden theory is a powerful geometric framework for many PDEs from fluid dynamics. In this paper we provide a toolbox to apply the Ebin-Marsden approach to stochastic PDE…
Stochastic control of the Landau-Lifshitz-Gilbert equation
Zdzisław Brzeźniak, Soham Gokhale, Utpal Manna
We consider the stochastic Landau-Lifshitz-Gilbert equation in dimension 1. A control process is added to the effective field. We show the existence of a weak martingale solution f…
Reflection of Stochastic Evolution Equations in Infinite Dimensional Domains
Zdzisław Brzeźniak, Tusheng Zhang
In this paper, we establish the existence and the uniqueness of solutions of stochastic evolution equations (SEEs) with reflection in an infinite dimensional ball. Our framework is…
Stochastic wave equations with constraints: well-posedness and Smoluchowski-Kramers diffusion approximation
Sandra Cerrai, Zdzislaw Brzeźniak
We investigate the well-posedness of a class of stochastic second-order in time damped evolution equations in Hilbert spaces, subject to the constraint that the solution lie within…
Statistical mechanics of the wave maps equation in dimension 1+1
Zdzisław Brzeźniak, Jacek Jendrej
We study wave maps with values in S^d, defined on the future light cone {|x| <= t}, with prescribed data at the boundary {|x| = t}. Based on the work of Keel and Tao, we prove that…
Sequential stability of weak martingale solutions to stochastic compressible Navier-Stokes equations with viscosity vanishing on vacuum
Zdzisław Brzeźniak, Gaurav Dhariwal, Ewelina Zatorska
In this paper, we investigate the compressible Navier-Stokes equations with degenerate, density-dependent, viscosity coefficient driven by multiplicative stochastic noise. We consi…
Large Deviations for -dimensional Stochastic Geometric Wave Equation
Zdzisław Brzeźniak, Ben Goldys, Martin Ondreját +1
We consider stochastic wave map equation on real line with solutions taking values in a -dimensional compact Riemannian manifold. We show first that this equation has unique, gl…
Ergodicity for stochastic equation of Navier--Stokes type
Z. Brzeźniak, T. Komorowski, S. Peszat
In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise…
Conservative interacting particles system with anomalous rate of ergodicity
Zdzislaw Brzeźniak, Franco Flandoli, Misha Neklyudov +1
We analyze certain conservative interacting particle system and establish ergodicity of the system for a family of invariant measures. Furthermore, we show that convergence rate to…