Related papers: Steady base states for Navier-Stokes granular hydr…
This paper is concerned with the evolution of two incompressible, immiscible fluids in two dimensions governed by the inhomogeneous Navier-Stokes equations. We prove global-in-time well-posedness, establishing the preservation of the…
Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…
We use dynamical systems theory to construct the normal form of the Navier--Stokes equations for the flow of a thin layer of fluid upon a solid substrate. The normal form equations illuminate the fluid dynamics by decoupling the long-term…
We propose a finite element discretization for the steady, generalized Navier-Stokes equations for fluids with shear-dependent viscosity, completed with inhomogeneous Dirichlet boundary conditions and an inhomogeneous divergence constraint.…
We study a general Navier-Stokes-Cahn-Hilliard-Boussinesq system that describes the motion of a mixture of two incompressible Newtonian fluids with thermo-induced Marangoni effects. The Cahn-Hilliard dynamics of the binary mixture is…
Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional Navier--Stokes equations on a sphere. The stationary flow on the sphere has two singularities (a sink and a source)…
The roll streak structure (RSS) is ubiquitous in shear flow turbulence and is fundamental to the dynamics of the self-sustaining process (SSP) maintaining the turbulent state. The formation and maintenance of the RSS in wall-bounded shear…
We study here the steady state attained in a granular gas of inelastic rough spheres that is subject to a spatially uniform random volume force. The stochastic force has the form of the so-called white noise and acts by adding impulse to…
Consider the stationary Boltzmann equation in 2D convex domains with diffusive boundary condition. In this paper, we establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier-Stokes-Fourier system…
In this paper, the Liouville-type theorems for the steady Navier-Stokes system are investigated. First, we prove that any bounded smooth helically symmetric solution in $\mathbb{R}^3$ must be a constant vector. Second, for steady…
We solve the relativistic Navier-Stokes equations with homogeneous boost-invariant boundary conditions, and perform a stability analysis of the solution. We show that, if the bulk viscosity has a peak around $T_c$ as inferred from QCD-based…
It is known that smooth solutions to the non-isentropic Navier-Stokes equations without heat-conductivity may lose their regularities in finite time in the presence of vacuum. However, in spite of the recent progress on such blowup…
Numerical schemes derived from gas-kinetic theory can be applied to simulations in the hydrodynamics limit, in laminar and also turbulent regimes. In the latter case, the underlying Boltzmann equation describes a distribution of eddies, in…
Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. To model this situation, we use a phase field…
We investigate a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn-Hilliard equation for the…
In the preceding paper, linear response methods have been applied to obtain formally exact expressions for the parameters of Navier-Stokes order hydrodynamics. The analysis there is general, applying to both normal and granular fluids with…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…
Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of…