Related papers: Existence theory for stochastic power law fluids
In the present work, we investigate stochastic third grade fluids equations in a $d$-dimensional setting, for $d = 2, 3$. More precisely, on a bounded and simply connected domain $\mathcal{D}$ of $\mathbb{R}^d$, $d = 2,3$, with a…
This work aims to control the dynamics of certain non-Newtonian fluids in a bounded domain of $\mathbb{R}^d$, $d=2,3$ perturbed by a multiplicative Wiener noise, the control acts as a predictable distributed random force, and the goal is to…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
Stochastic non-local conservation law equation in the presence of discontinuous flux functions is considered in an $L^{1}\cap L^{2}$ setting. The flux function is assumed bounded and integrable (spatial variable). Our result is to prove…
In this paper, we consider a kind of fully coupled slow fast motion, in which the slow variable satisfies the non Lipschitz condition. We prove that the stochastic flow of the slow variable exists and moreover, satisfies the large deviation…
We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically $(s-1)$-growth with the parameter $s$…
This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for weakly viscoelastic fluid flows in $\R^N$ or $\T^N$ for…
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii)…
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…
We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…
In this paper we consider the three-dimensional compressible MHD system with stochastic external forces in a bounded domain. We obtain the existence of martingale solution which is a weak solution for the fluid variables, the Brownian…
In this study, we investigate the incompressible generalised Navier-Stokes-Voigt equations within a bounded domain $\Omega \subset \mathbb{R}^d$, where $d \geq 2$. The governing momentum equation is expressed as: $$…
We prove the existence of weak solutions to steady, compressible non-Newtonian Navier-Stokes system on a bounded, two- or three-dimensional domain. Assuming the viscous stress tensor is monotone satisfying a power-law growth with power $r$…
In this paper we present a mathematical analysis for a steady-state laminar boundary layer flow, governed by the Ostwald-de Wael power-law model of an incompressible non- Newtonian fluid past a semi-infinite power-law stretched flat plate…
We consider a viscous incompressible fluid interacting with a linearly elastic shell of Koiter type which is located at some part of the boundary. Recently models with stochastic perturbation in the shell equation have been proposed in the…
We investigate a system of nonlinear partial differential equations modeling the unsteady flow of a shear-thinning non-Newtonian fluid with a concentration-dependent power-law index. The system consists of the generalized Navier-Stokes…
We provide existence of very weak solutions and new a-priori estimates for steady flows of non-Newtonian fluids when the right-hand sides are not in the natural existence class. To obtain the a-priori estimates we make use of a newly…
In this paper we study a nonlinear stochastic fluid-structure interaction problem with a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a…
We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\varepsilon ^2$. When $\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift…
We investigate the Navier-Stokes turbulence driven by a stochastic random Gaussian force. Using a field-theoretic approach, we uncover an anomaly that brings hidden structure to the theory. The anomaly is generated by a non-self-adjoint…