Related papers: The Navier-Stokes limit of kinetic equations for l…
In 2001, H. Koch and D. Tataru proved the existence of global in time solutions to the incompressible Navier-Stokes equations in ${\mathbb{R}}^d$ for initial data small enough in $BMO^{-1}$. We show in this article that the Koch and Tataru…
We are concerned with the inviscid limit of the Navier-Stokes equations on bounded regular domains in $\mathbb{R}^3$ with the kinematic and Navier boundary conditions. We first establish the existence and uniqueness of strong solutions in…
We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…
We present a short and elegant proof of an estimate for the pressure in terms of the velocity and external data in bounded domains under the slip and Navier boundary conditions. We also show an application of this result for conditional…
In the continuum flow regime, the Navier-Stokes equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied gas dynamics. Both equations are constructed from modeling…
In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the support of general meshes, possibly including polygonal or…
We prove some criteria for the convergence of weak solutions of the 2D incompressible Navier-Stokes equations with Navier slip boundary conditions to a strong solution of incompressible Euler. The slip rate depends on a power of the…
We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an…
We consider the modified Navier-Stokes equations in R3 describing the motion of a fluid in the presence of a rotating rigid body. Weighted Sobolev spaces are used to describe the behavior of solutions at large distances. Under suitable…
This paper exposes how to obtain a relation that have to be hold for all free--divergence velocity fields that evolve according to Navier--Stokes equations. However, checking the violation of this relation requires a huge computational…
We prove existence of global-in-time weak solutions of the incompressible Navier-Stokes equations in the half-space $\mathbb{R}^3_+$ with initial data in a weighted space that allow non-uniformly locally square integrable functions that…
We consider the Cauchy problem for the incompressible Navier--Stokes equations on the whole space $\mathbb{R}^3$, with initial value $\vec u_0\in {\rm BMO}^{-1}$ (as in Koch and Tataru's theorem) and with force $\vec f=\Div \mathbb{F}$…
The global classical solution to the incompressible Navier-Stokes-Fourier equation with small initial data in the whole space is constructed through a zero Knudsen number limit from the solutions to the Boltzmann equation with general…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
We address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the…
We investigate the three-dimensional incompressible Navier-Stokes equations. The equations are discretized with Fourier spectral method and a fourth-order Runge-Kutta scheme in time. The spectral accuracy, resolution conditions, and an…
This paper investigates the isentropic compressible Navier-Stokes equations on k-connected domains under Navier-slip boundary conditions. We study the multi-solvability of the stationary systems on general domains, which is closely related…
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…
In the note, a new regularity condition for axisymmetric solutions to the non-stationary 3D Navier-Stokes equations is proven. It is slightly supercritical.
In this paper, we utilize some series and an iterative method to solve some Navier-Stokes equations with the initial conditions being some complex-valued periodic functions on $R^3$. Then a new strategy for dealing with the conjecture of…