Related papers: Asymmetric and Moving-Frame Approaches to Navier-S…
We make an exposition of recent research on $(-1)$-homogeneous solutions of the three-dimensional incompressible stationary Navier-Stokes equations with singular rays. We also discuss properties of such solutions that are axisymmetric with…
New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of…
The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large…
We establish the incompressible Navier--Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian.…
The scale factors of an arbitrary orthogonal space are a measure of its content of homogeneous orthogonal space. In the present study, it is shown, that their spatial and temporal rates of variation do not contribute to the differential…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
The problems of numerical modeling of viscous incompressible fluid flows are widely considered in computational fluid dynamics. Stationary solutions of boundary value problems for the Navier-Stokes equations exist at large Reynolds numbers,…
Recently there has been an increasing interest for a better understanding of ultra low Reynolds number flows. In this context we present a new setup which allows to efficiently solve the stationary incompressible Navier-Stokes equations in…
This paper discussed the global existence of the smoothing solution for the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant coefficients.…
Resolvent analysis of the linearized Navier-Stokes equations provides useful insight into the dynamics of transitional and turbulent flows and can provide a model for the dominant coherent structures within the flow, particularly for flows…
The volume penalty method provides a simple, efficient approach for solving the incompressible Navier-Stokes equations in domains with boundaries or in the presence of moving objects. Despite the simplicity, the method is typically limited…
The resolvent formulation of the Navier$\text{--}$Stokes equations gives a means for the characterization and prediction of features of turbulent flows$\text{---}$such as statistics, structures and their nonlinear…
Several new families of nonlinear three-dimensional travelling wave solutions to the Navier-Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures…
We present and analyze a fully discrete fractional time stepping technique for the solution of the micropolar Navier Stokes equations, which is a system of equations that describes the evolution of an incompressible fluid whose material…
The incompressible Navier-Stokes equations and static Euler equations are considered. We find that there exist infinite non-trivial regular solutions of incompressible static Euler equations with given boundary conditions. Moreover there…
We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field $v$ satisfying randomly forced Navier-Stokes equations, leading to…
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…
In this paper, we study the Navier-Stokes equations of compressible, barotropic flow posed in a bounded set in $\mathbb{R}^3$ with different boundary conditions. Specifically, we prove that the local-in-time smooth solution of the…
We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we…
We study the nonhomogeneous boundary value problem for the Navier-Stokes equations of steady motion of a viscous incompressible fluid in arbitrary bounded multiply connected plane or axially-symmetric spatial domains. We prove that this…