Related papers: On the Navier-Stokes equation perturbed by rough t…
We study the Navier-Stokes equations on a smooth bounded domain $D\subset \mathbb R^d$ ($d=2$ or 3), under the effect of an additive fractional Brownian noise. We show local existence and uniqueness of a mild $L^p$-solution for $p>d$.
In this article, we investigate an interacting particle system featuring random intensities, individual noise, and environmental noise, commonly referred to as stochastic point vortex model. The model serves as an approximation for the…
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…
We investigate the Cauchy problem for a quasilinear equation with transport rough input of the form $\mathrm{d} u-\partial_i(a^{ij}(u)\partial_j u)\mathrm{d} t =\mathrm{d} \mathbf{X}_t^i(x)\partial_i u_t,$ $u_0\in L^2$ on the torus $\mathbb…
It is a classical problem in fluid dynamics about the stability and instability of different hydrodynamic patterns in various physical settings, in particular in the high Reynolds number limit of laminar flow with boundary layer. However,…
This study is devoted to the incompressible and stationary Navier-Stokes equations in two-dimensional unbounded domains. First, the main results on the construction of the weak solutions and on their asymptotic behavior are reviewed and…
In this paper, we analyze the behavior of viscous shock profiles of one-dimensional compressible Navier-Stokes equations with a singular pressure law which encodes the effects of congestion. As the intensity of the singular pressure tends…
We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these…
We give a geometric approach to proving know regularity and existence theorems for the 2D Navier-Stokes Equations. We feel this point of view is instructive in better understanding the dynamics. The technique is inspired by constructions in…
We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…
In this paper we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the…
In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible fluid in a bounded domain of the plane. The first system corresponds to an inviscid fluid driven by the Euler equation whereas the other one…
The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier-Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
We introduce a new modified Navier-Stokes model in $3$ dimensions by modifying the convection term in the ordinary Navier-Stokes equations. This is done by replacing the convective term $(\textbf{u}\cdot \nabla) \textbf{u}$ by…
In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical measure associated with the particle system converges…
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…
A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…
Martingale solutions of stochastic Navier-Stokes equations in 2D and 3D possibly unbounded domains, driven by the L\'evy noise consisting of the compensated time homogeneous Poisson random measure and the Wiener process are considered.…
We consider the Navier-Stokes system describing the motion of a compressible barotropic fluid driven by stochastic external forces. Our approach is semi-deterministic, based on solving the system for each fixed representative of the random…