Related papers: Uniqueness for a Stochastic Inviscid Dyadic Model
Recently, a concept of deterministic and stochastic turbulence has been introduced based on experiments with a boundary layer. In these experiments, the flow was driven with controlled random perturbation; in addition, natural ambient noise…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
We consider the classical two-dimensional Rosenzweig-MacArthur prey-predator model with a degenerate noise, whereby only the prey variable is subject to small environmental fluctuations. This model has already been introduced in…
A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…
Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…
In this paper, we study a simple hydrodynamical model showing abrupt flow reversals at random times. For a suitable range of parameters, we show that the dynamics of flow reversal is accurately described by stochastic differential…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
In this paper, we prove the global existence and singularity formation for a wave system from modelling nematic liquid crystals in one space dimension. In our model, although the viscous damping term is included, the solution with smooth…
In this work we prove the existence and uniqueness of the strong solution of the shell model of turbulence perturbed by L\'{e}vy noise. The local monotonicity arguments have been exploited in the proofs.
This paper concerns with the compressible two-fluid model with algebraic pressure closure. We prove a conditional weak-strong uniqueness principle, meaning that a finite energy weak solution, with bounded densities, coincides with the…
A class of dynamical models of turbulence living on a one-dimensional dyadic-tree structure is introduced and studied. The models are obtained as a natural generalization of the popular GOY shell model of turbulence. These models are found…
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions…
We study an infinite system of non-linear differential equations coupled in a tree-like structure. This system was previously introduced in the literature and it is the model from which the dyadic shell model of turbulence was derived. It…
In this paper, we consider the well-posedness of the weakly damped stochastic nonlinear Schr\"odinger(NLS) equation driven by multiplicative noise. First, we show the global existence of the unique solution for the damped stochastic NLS…
We study a class of ordinary differential equations with a non-Lipschitz point singularity, which admit non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on the parameter…
The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the $L^2$-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq…
We present a simple dynamical model to address the question of introducing a stochastic nature in a time variable. This model includes noise in the time variable but not in the "space" variable, which is opposite to the normal description…
We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in…