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pro vyhledávání: '"Ferrario, Benedetta"'
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
We establish the uniqueness and the asymptotic stability of the invariant measure for the two dimensional Navier Stokes equations driven by a multiplicative noise which is either bounded or with a sublinear or a linear growth. We work on an effective
Externí odkaz:
http://arxiv.org/abs/2307.03483
We construct stationary statistical solutions of a deterministic unforced nonlinear Schr\"odinger equation, by perturbing it by a linear damping $\gamma u$ and a stochastic force whose intensity is proportional to $\sqrt \gamma$, and then letting $\g
Externí odkaz:
http://arxiv.org/abs/2305.10393
We study the nonlinear Schr\"odinger equation with linear damping, i.e. a zero order dissipation, and additive noise. Working in $R^d$ with d = 2 or d = 3, we prove the uniqueness of the invariant measure when the damping coefficient is sufficiently
Externí odkaz:
http://arxiv.org/abs/2205.13364
We consider a stochastic nonlinear defocusing Schr\"{o}dinger equation with zero-order linear damping, where the stochastic forcing term is given by a combination of a linear multiplicative noise in the Stratonovich form and a nonlinear noise in the
Externí odkaz:
http://arxiv.org/abs/2106.07043
Autor:
Bessaih, Hakima, Ferrario, Benedetta
We study the two-dimensional Euler equations, damped by a linear term and driven by an additive noise. The existence of weak solutions has already been studied; pathwise uniqueness is known for solutions that have vorticity in $L^\infty$. In this pap
Externí odkaz:
http://arxiv.org/abs/1909.00424
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Autor:
Ferrario, Benedetta
Publikováno v:
In Journal of Differential Equations 5 January 2023 342:1-20
We consider the Navier-Stokes equations in vorticity form in $\mathbb{R}^2$ with a white noise forcing term of multiplicative type, whose spatial covariance is not regular enough to apply the It\^o calculus in $L^q$ spaces, $1
Externí odkaz:
http://arxiv.org/abs/1803.01799
Publikováno v:
Annali di Matematica Pura ed Applicata 2018
We consider the Navier-Stokes equation on the 2D torus, with a stochastic forcing term which is a cylindrical fractional Wiener noise of Hurst parameter $H$. Following [3,8] which dealt with the case $1/2$, we prove a local existence and uniqueness r
Externí odkaz:
http://arxiv.org/abs/1802.08623