Zobrazeno 1 - 10
of 293
pro vyhledávání: '"Brzeźniak, Zdzisław"'
The Voigt regularization is a technique used to model turbulent flows, offering advantages such as sharing steady states with the Navier-Stokes equations and requiring no modification of boundary conditions; however, the parabolic dissipative charact
Externí odkaz:
http://arxiv.org/abs/2410.23492
Autor:
Brzeźniak, Zdzisław, Ferrari, Matteo
We prove the existence and some moment estimates for an invariant measure $\mu$ for the two-dimensional ($2$D) deterministic Euler equations on the unbounded domain $\mathbb R^2$ and with highly regular initial data. The result is achieved by first s
Externí odkaz:
http://arxiv.org/abs/2409.17697
We consider the nonlinear Schr\"odinger equation on the $d$-dimensional torus $\mathbb T^d$, with the nonlinearity of polynomial type $|u|^{2\sigma}u$. For any $\sigma \in \mathbb N$ and $s>\frac d2$ we prove that adding to this equation a suitable s
Externí odkaz:
http://arxiv.org/abs/2406.19214
Autor:
Brzeźniak, Zdzisław, Rana, Nimit
Publikováno v:
Comptes Rendus. Mathématique, Vol 358, Iss 6, Pp 633-639 (2020)
We announce a result on the existence of a unique local solution to a stochastic geometric wave equation on the one dimensional Minkowski space $\mathbb{R}^{1+1}$ with values in an arbitrary compact Riemannian manifold. We consider a rough initial da
Externí odkaz:
https://doaj.org/article/46a3413cf17f4e9c9ca064c6446b8a6d
This paper aims to establish the local and global well-posedness theory in $L^1$, inspired by the approach of Keel and Tao [Internat. Math. Res. Notices, 1998], for the forced wave map equation in the ``external'' formalism. In this context, the targ
Externí odkaz:
http://arxiv.org/abs/2404.09195
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 important role.
Externí odkaz:
http://arxiv.org/abs/2403.01125
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 PDEs, combining tools from infinite-dimensional geometry and stochastic a
Externí odkaz:
http://arxiv.org/abs/2311.08197
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 for the resulting controlled equation. The proof uses the classical Fae
Externí odkaz:
http://arxiv.org/abs/2309.10260
Autor:
Brzeźniak, Zdzisław, Zhang, Tusheng
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 sufficiently general to include e.g. the stochastic Navier-Stokes equ
Externí odkaz:
http://arxiv.org/abs/2309.01251
Autor:
Cerrai, Sandra, Brzeźniak, Zdzislaw
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 the unitary sphere. Then, we focus on a specific example, the stochas
Externí odkaz:
http://arxiv.org/abs/2303.09717