Related papers: The Incompressible Non-Relativistic Navier-Stokes …
A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the…
Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation…
The motion of water is governed by the Navier-Stokes equations, which are complemented by the continuity equation to ensure local mass conservation. In this work, we construct the relativistic generalization of these equations through a…
We establish the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for three-dimensional compressible isentropic flow in the whole space. It is shown that there exists a unique regular solution of compressible…
Relativistic Navier-Stokes equations express the conservation of the energy-momentum tensor and the particle number current in terms of the local hydrodynamic variables: temperature, fluid velocity, and the chemical potential. We show that…
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…
In the realm of mathematical fluid dynamics, a formidable challenge lies in establishing inviscid limits from the Navier-Stokes equations to the Euler equations, wherein physically admissible solutions can be discerned. The pursuit of…
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,…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…
Systems of hydrodynamic type equations derived from the Navier-Stokes equations and the boundary layer equations are considered. A transformation of the Crocco type reducing the equation order for the longitudinal velocity component is…
Introduction: the Navier-Stokes equations are essential in fluid dynamics, describing the motion of fluids like liquids and gases. Solving these equations, especially in complex flows and high-Reynolds-number regimes, is a significant…
Shockwaves provide a useful and rewarding route to the nonequilibrium properties of simple fluids far from equilibrium. For simplicity, we study a strong shockwave in a dense two-dimensional fluid. Here, our study of nonlinear transport…
The fluid-gravity correspondence provides us with explicit spacetime metrics that are holographically dual to (non-)relativistic nonlinear hydrodynamics. The vacuum Einstein equations, in the presence of a Killing vector, possess…
We analyze the two-dimensional incompressible Navier-Stokes equations on a smooth, bounded domain with Navier boundary conditions. Starting from an initial vorticity in $L^p$ with $p>2$, we show strong convergence of the vorticity in the…
Convergence of particle systems to the Vlasov-Navier-Stokes equations is a difficult topic with only fragmentary results. Under a suitable modification of the classical Stokes drag force interaction, here a partial result in this direction…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit…
These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…
We have developed dynamic manifold solutions for the Navier-Stokes equations using an extension of differential geometry called the calculus for moving surfaces. Specifically, we have shown that the geometric solutions to the Navier-Stokes…