相关论文: Space and time analyticity for inviscid equations …
In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We…
We show that a Galilean invariant version of fluid dynamics can be derived by the methods of statistical dynamics using Maxwell's balance equations. The basic equation is non-local, and might replace Boltzmann's equation if the latter turns…
We study the behaviour of the solution $u_\varepsilon$ to the Navier-Stokes equations with vanishing viscosity and a non-slip condition in a randomly perforated domain. We consider the space $\mathbb{R}^3$ where we remove $N$ holes that are…
We show that, for a given H\"older continuous curve in $\{(\gamma(t),t)\,:\, t>0\} \subset R^3\times R^+$, there exists a solution to the Navier-Stokes system for an incompressible fluid in $R^3$ which is smooth outside this curve and…
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…
We consider the limit $\alpha\to0$ for a second grade fluid on a bounded domain with Dirichlet boundary conditions. We show convergence towards a solution of the Navier-Stokes equations under two different types of hypothesis on the initial…
We prove that the multidimensional dimensional initial value problem for the Navier-Stokes equations is globally well-posed in the so-called Moment and Grand Lebesgue Spaces (GLS), and give some a priory estimations for solution in this…
An asymptotic expansion at spatial infinity of a weak time-periodic solution to the Navier-Stokes equations with a non-zero drift term in the three-dimensional whole-space is carried out. The asymptotic profile is explicitly identified and…
We introduce a special stochastic perturbation of the flow of diffuse matter as a curve in the group of diffeomorphisms of flat n-dimensional torus such that the perturbed system yields a solution of Burgers equation in the tangent space at…
The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods…
Euler and Navier-Stokes have variant systems with dynamical invariance of helicity and thus (weak) topological equivalence, allowing a strong `frozen-in' (to, or, dually, `Lie-carried' by the \textit{virtual} velocity $V$) formulation of…
The paper addresses an error analysis of an Eulerian finite element method used for solving a linearized Navier--Stokes problem in a time-dependent domain. In this study, the domain's evolution is assumed to be known and independent of the…
We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…
This is a rather comprehensive study on the dynamics of Navier-Stokes and Euler equations via a combination of analysis and numerics. We focus upon two main aspects: (a). zero viscosity limit of the spectra of linear Navier-Stokes operator,…
This article offers a modern perspective which exposes the many contributions of Leray in his celebrated work on the Navier--Stokes equations from 1934. Although the importance of his work is widely acknowledged, the precise contents of his…
In the current state of the art regarding the Navier--Stokes equations, the existence of unique solutions for incompressible flows in two spatial dimensions is already well-established. Recently, these results have been extended to models…
The goal of this note is to demonstrate that as soon as the hyper-diffusion exponent is greater than one, a class of finite time blow-up scenarios consistent with the analytic structure of the flow (prior to the possible blow-up time) can…
We study the long-time behavior of spatially periodic solutions of the Navier-Stokes equations in the three-dimensional space. The body force is assumed to possess an asymptotic expansion or, resp., finite asymptotic approximation, in…
The present paper is motivated by recent mathematical work on the incompressible Euler and Navier-Stokes equations, partly having physically problematic results and unrealistic expectations. The Euler and Navier-Stokes equations are…
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…